Log in

Relevant bibliographies by topics / Isometrics (Mathematics) Banach spaces / Dissertations / Theses

To see the other types of publications on this topic, follow the link: Isometrics (Mathematics) Banach spaces.

Dissertations / Theses on the topic 'Isometrics (Mathematics) Banach spaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 dissertations / theses for your research on the topic 'Isometrics (Mathematics) Banach spaces.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.

1

Cowell, Simon Kalton Nigel J. "Asymptotic unconditionality in Banach spaces." Diss., Columbia, Mo. : University of Missouri--Columbia, 2009. http://hdl.handle.net/10355/6149.

Full text

Abstract:

Title from PDF of title page (University of Missouri--Columbia, viewed on Feb. 20, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Professor Nigel J. Kalton. Vita. Includes bibliographical references.

APA, Harvard, Vancouver, ISO, and other styles

2

Shao, Chuang Gao Su. "Urysohn ultrametric spaces and isometry groups." [Denton, Tex.] : University of North Texas, 2009. http://digital.library.unt.edu/permalink/meta-dc-9918.

Full text

APA, Harvard, Vancouver, ISO, and other styles

3

West, Graeme Philip. "Non-commutative Banach function spaces." Master's thesis, University of Cape Town, 1990. http://hdl.handle.net/11427/17117.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Gowers, William T. "Symmetric structures in Banach spaces." Thesis, University of Cambridge, 1990. https://www.repository.cam.ac.uk/handle/1810/252814.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Kalaichelvan, Rajendra. "Function spaces and a problem of banach." Doctoral thesis, University of Cape Town, 2000. http://hdl.handle.net/11427/4895.

Full text

Abstract:

Bibliography: leaves 87-90.<br>Function spaces have been a useful tool in probing the convergence of sequences of functions. The theory seems to have been triggered off by the works of Ascoli [36], Arzelà [37] and Hadamard [38]. In this thesis, we consider the space of continuous functions from a topological space X into the reals R, which we denote C(X).

APA, Harvard, Vancouver, ISO, and other styles

6

Doré, Michael J. "Universal Fréchet sets in Banach spaces." Thesis, University of Warwick, 2010. http://wrap.warwick.ac.uk/3688/.

Full text

Abstract:

We define a universal Fréchet set S of a Banach space Y as a subset containing a point of Fréchet differentiability of every Lipschitz function g : Y -> R. We prove a sufficient condition for S to be a universal Fréchet set and use this to construct new examples of such sets. The strongest such result says that in a non-zero Banach space Y with separable dual one can find a universal Fréchet set S ⊆ Y that is closed, bounded and has Hausdorff dimension one.

APA, Harvard, Vancouver, ISO, and other styles

7

Zheng, Bentuo. "Embeddings and factorizations of Banach spaces." [College Station, Tex. : Texas A&M University, 2007. http://hdl.handle.net/1969.1/ETD-TAMU-1551.

Full text

APA, Harvard, Vancouver, ISO, and other styles

8

Blagojevic, Danilo. "Spectral families and geometry of Banach spaces." Thesis, University of Edinburgh, 2007. http://hdl.handle.net/1842/2389.

Full text

Abstract:

The principal objects of study in this thesis are arbitrary spectral families, E, on a complex Banach space X. The central theme is the relationship between the geometry of X and the p-variation of E. We show that provided X is super- reflexive, then given any E, there exists a value 1 Â· p < 1, depending only on E and X, such that var p(E) < 1. If X is uniformly smooth we provide an explicit range of such values p, which depends only on E and the modulus of convexity of X*, delta X*(.).

APA, Harvard, Vancouver, ISO, and other styles

9

Ochoa, James Philip. "Tensor Products of Banach Spaces." Thesis, University of North Texas, 1996. https://digital.library.unt.edu/ark:/67531/metadc278580/.

Full text

Abstract:

Tensor products of Banach Spaces are studied. An introduction to tensor products is given. Some results concerning the reciprocal Dunford-Pettis Property due to Emmanuele are presented. Pelczyriski's property (V) and (V)-sets are studied. It will be shown that if X and Y are Banach spaces with property (V) and every integral operator from X into Y* is compact, then the (V)-subsets of (X⊗F)* are weak* sequentially compact. This in turn will be used to prove some stronger convergence results for (V)-subsets of C(Ω,X)*.

APA, Harvard, Vancouver, ISO, and other styles

10

Sarantopoulos, I. C. "Polynomials and multilinear mappings in Banach spaces." Thesis, Brunel University, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376057.

Full text

APA, Harvard, Vancouver, ISO, and other styles

11

Dymond, Michael Robert. "Differentiability and negligible sets in Banach spaces." Thesis, University of Birmingham, 2014. http://etheses.bham.ac.uk//id/eprint/5158/.

Full text

Abstract:

A set S in a Banach space X is called a universal differentiability set if S contains a point of differentiability of every Lipschitz function f : X -> R. The present thesis investigates the nature of such sets. We uncover examples of exceptionally small universal differentiability sets and prove that all universal differentiability sets satisfy certain strong structural conditions. Later, we expand our focus to properties of more general absolutely continuous functions.

APA, Harvard, Vancouver, ISO, and other styles

12

Jeganathan, P. "Fixed points for nonexpansive mappings in Banach spaces." Master's thesis, University of Cape Town, 1991. http://hdl.handle.net/11427/17067.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Obeid, Ossama A. "Property (H*) and Differentiability in Banach Spaces." Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc277852/.

Full text

Abstract:

A continuous convex function on an open interval of the real line is differentiable everywhere except on a countable subset of its domain. There has been interest in the problem of characterizing those Banach spaces where the continuous functions exhibit similar differentiability properties. In this paper we show that if a Banach space E has property (H*) and B_E• is weak* sequentially compact, then E is an Asplund space. In the case where the space is weakly compactly generated, it is shown that property (H*) is equivalent for the space to admit an equivalent Frechet differentiable norm. Moreover, we define the SH* spaces, show that every SH* space is an Asplund space, and show that every weakly sequentially complete SH* space is reflexive. Also, we study the relation between property (H*) and the asymptotic norming property (ANP). By a slight modification of the ANP we define the ANP*, and show that if the dual of a Banach spaces has the ANP*-I then the space admits an equivalent Fréchet differentiability norm, and that the ANP*-II is equivalent to the space having property (H*) and the closed unit ball of the dual is weak* sequentially compact. Also, we show that in the dual of a weakly countably determined Banach space all the ANP-K'S are equivalent, and they are equivalent for the predual to have property (H*).

APA, Harvard, Vancouver, ISO, and other styles

14

Al-Nayef, Anwar Ali Bayer, and mikewood@deakin edu au. "Semi-hyperbolic mappings in Banach spaces." Deakin University. School of Computing and Mathematics, 1997. http://tux.lib.deakin.edu.au./adt-VDU/public/adt-VDU20051208.110247.

Full text

Abstract:

The definition of semi-hyperbolic dynamical systems generated by Lipschitz continuous and not necessarily invertible mappings in Banach spaces is presented in this thesis. Like hyperbolic mappings, they involve a splitting into stable and unstable spaces, but a slight leakage from the strict invariance of the spaces is possible and the unstable subspaces are assumed to be finite dimensional. Bi-shadowing is a combination of the concepts of shadowing and inverse shadowing and is usually used to compare pseudo-trajectories calculated by a computer with the true trajectories. In this thesis, the concept of bi-shadowing in a Banach space is defined and proved for semi-hyperbolic dynamical systems generated by Lipschitz mappings. As an application to the concept of bishadowing, linear delay differential equations are shown to be bi-shadowing with respect to pseudo-trajectories generated by nonlinear small perturbations of the linear delay equation. This shows robustness of solutions of the linear delay equation with respect to small nonlinear perturbations. Complicated dynamical behaviour is often a consequence of the expansivity of a dynamical system. Semi-hyperbolic dynamical systems generated by Lipschitz mappings on a Banach space are shown to be exponentially expansive, and explicit rates of expansion are determined. The result is applied to a nonsmooth noninvertible system generated by delay differential equation. It is shown that semi-hyperbolic mappings are locally φ-contracting, where -0 is the Hausdorff measure of noncompactness, and that a linear operator is semi-hyperbolic if and only if it is φ-contracting and has no spectral values on the unit circle. The definition of φ-bi-shadowing is given and it is shown that semi-hyperbolic mappings in Banach spaces are φ-bi-shadowing with respect to locally condensing continuous comparison mappings. The result is applied to linear delay differential equations of neutral type with nonsmooth perturbations. Finally, it is shown that a small delay perturbation of an ordinary differential equation with a homoclinic trajectory is chaotic.

APA, Harvard, Vancouver, ISO, and other styles

15

Groves, James Stuart. "A study of stochastic processes in Banach spaces." Thesis, Lancaster University, 2000. http://eprints.lancs.ac.uk/125004/.

Full text

Abstract:

The theory of 2-convex norms is applied to Banach space valued random vectors. Use is made of a norm on random vectors, introduced by Pisier, equal to the 2-absolutely summing norm on an associated space of operators. For Q the variance of some centred Gaussian random vector in a separable Banach space it is shown that, necessarily, Q factors through l2 as a product of 2-summing operators. This factorisation condition is sufficient when the Banach space is of Gaussian type 2. The stochastic integral of a family of operators with respect to a cylindrical Q-Wiener process is shown to exist under a Hölder continuity condition involving the 2-summing norm. A Langevin equation dZt + ΛZtdt = dBt with values in a separable Banach space is studied. The operator Λ is closed and densely defined. A weak solution (Zt ; Bt), where Zt is centred, Gaussian and stationary while Bt is a Q-Wiener process, is given when iΛ and iΛ* generate C0 groups and the resolvent of Λ is uniformly bounded on the imaginary axis. Both Zt and Bt are stochastic integrals with respect to a spectral Q-Wiener process. The convolution of two arcsine probability densities is shown to be an elliptic integral. Ensembles (Xn)n≥1 of random Hermitian matrices are considered. Each Xn is n by n with distribution invariant under unitary conjugation and induced by a positive weight function on R. New proofs are given of results, due to Boutet de Monvel, Pastur, Shcherbina and Sodin, on the behaviour of the empirical distribution of the eigenvalues of Xn as n tends to infinity. Results in analytic function theory are proved. An H∞ interpolating sequence in the disc D whose Horowitz product does not lie in the Bergman space L2a(D) is exhibited. A condition satisfied by Banach spaces of non-trivial analytic Lusin cotype is obtained.

APA, Harvard, Vancouver, ISO, and other styles

16

Shao, Chuang. "Urysohn ultrametric spaces and isometry groups." Thesis, University of North Texas, 2009. https://digital.library.unt.edu/ark:/67531/metadc9918/.

Full text

Abstract:

In this dissertation we study a special sub-collection of Polish metric spaces: complete separable ultrametric spaces. Polish metric spaces have been studied for quite a long while, and a lot of results have been obtained. Motivated by some of earlier research, we work on the following two main parts in this dissertation. In the first part, we show the existence of Urysohn Polish R-ultrametric spaces, for an arbitrary countable set R of non-negative numbers, including 0. Then we give point-by-point construction of a countable R-ultra-Urysohn space. We also obtain a complete characterization for the set R which corresponding to a R-Urysohn metric space. From this characterization we conclude that there exist R-Urysohn spaces for a wide family of countable R. Moreover, we determine the complexity of the classification of all Polish ultrametric spaces. In the second part, we investigate the isometry groups of Polish ultrametric spaces. We prove that isometry group of an Urysohn Polish R-ultrametric space is universal among isometry groups of Polish R-ultrametric spaces. We completely characterize the isometry groups of finite ultrametric spaces and the isometry groups of countable compact ultrametric spaces. Moreover, we give some necessary conditions for finite groups to be isomorphic to some isometry groups of finite ultrametric spaces.

APA, Harvard, Vancouver, ISO, and other styles

17

Boos, Lynette J. "Function Algebras on Riemann Surfaces and Banach Spaces." Bowling Green State University / OhioLINK, 2006. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1151340555.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Doust, Ian Raymond. "Well-bounded operators and the geometry of Banach spaces." Thesis, University of Edinburgh, 1988. http://hdl.handle.net/1842/13705.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

de, Mendonca Braga Bruno. "On the Borel Complexity of some classes of Banach spaces." Thesis, Kent State University, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3618917.

Full text

Abstract:

<p> In this dissertation I mainly study several classes of Banach spaces and I try to compute, of at least to obtain a lower/upper bound, to its Borel complexity. Also, using those results, we show some non-universality results for some of those classes of Banach spaces.</p>

APA, Harvard, Vancouver, ISO, and other styles

20

Bihun, Oksana Chicone Carmen Charles. "Approximate isometries and distortion energy functionals." Diss., Columbia, Mo. : University of Missouri--Columbia, 2009. http://hdl.handle.net/10355/6129.

Full text

Abstract:

Title from PDF of title page (University of Missouri--Columbia, viewed on Feb. 11, 2010). The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. Dissertation advisor: Professor Carmen Chicone. Vita. Includes bibliographical references.

APA, Harvard, Vancouver, ISO, and other styles

21

Hume, David S. "Embeddings of infinite groups into Banach spaces." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:e38f58ec-484c-4088-bb44-1556bc647cde.

Full text

Abstract:

In this thesis we build on the theory concerning the metric geometry of relatively hyperbolic and mapping class groups, especially with respect to the difficulty of embedding such groups into Banach spaces. In Chapter 3 (joint with Alessandro Sisto) we construct simple embeddings of closed graph manifold groups into a product of three metric trees, answering positively a conjecture of Smirnov concerning the Assouad-Nagata dimension of such spaces. Consequently, we obtain optimal embeddings of such spaces into certain Banach spaces. The ideas here have been extended to other closed three-manifolds and to higher dimensional analogues of graph manifolds. In Chapter 4 we give an explicit method of embedding relatively hyperbolic groups into certain Banach spaces, which yields optimal bounds on the compression exponent of such groups relative to their peripheral subgroups. From this we deduce that the fundamental group of every closed three-manifold has Hilbert compression exponent one. In Chapter 5 we prove that relatively hyperbolic spaces with a tree-graded quasi-isometry representative can be characterised by a relative version of Manning's bottleneck property. This applies to the Bestvina-Bromberg-Fujiwara quasi-trees of spaces, yielding an embedding of each mapping class group of a closed surface into a finite product of simplicial trees. From this we obtain explicit embeddings of mapping class groups into certain Banach spaces and deduce that these groups have finite Assouad-Nagata dimension. It also applies to relatively hyperbolic groups, proving that such groups have finite Assouad-Nagata dimension if and only if each peripheral subgroup does.

APA, Harvard, Vancouver, ISO, and other styles

22

Jiang, Jiaosheng. "Bounded operators without invariant subspaces on certain Banach spaces." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3037506.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Sbeih, Reema. "NON-LINEAR MAPS BETWEEN SUBSETS OF BANACH SPACES." Kent State University / OhioLINK, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=kent1251217291.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Tarbard, Matthew. "Operators on Banach spaces of Bourgain-Delbaen type." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:4be220be-9347-48a1-85e6-eb0a30a8d51a.

Full text

Abstract:

The research in this thesis was initially motivated by an outstanding problem posed by Argyros and Haydon. They used a generalised version of the Bourgain-Delbaen construction to construct a Banach space $XK$ for which the only bounded linear operators on $XK$ are compact perturbations of (scalar multiples of) the identity; we say that a space with this property has very few operators. The space $XK$ possesses a number of additional interesting properties, most notably, it has $ell_1$ dual. Since $ell_1$ possesses the Schur property, weakly compact and norm compact operators on $XK$ coincide. Combined with the other properties of the Argyros-Haydon space, it is tempting to conjecture that such a space must necessarily have very few operators. Curiously however, the proof that $XK$ has very few operators made no use of the Schur property of $ell_1$. We therefore arrive at the following question (originally posed in cite{AH}): must a HI, $mathcal{L}_{infty}$, $ell_1$ predual with few operators (every operator is a strictly singular perturbation of $lambda I$) necessarily have very few operators? We begin by giving a detailed exposition of the original Bourgain-Delbaen construction and the generalised construction due to Argyros and Haydon. We show how these two constructions are related, and as a corollary, are able to prove that there exists some $delta > 0$ and an uncountable set of isometries on the original Bourgain-Delbaen spaces which are pairwise distance $delta$ apart. We subsequently extend these ideas to obtain our main results. We construct new Banach spaces of Bourgain-Delbaen type, all of which have $ell_1$ dual. The first class of spaces are HI and possess few, but not very few operators. We thus have a negative solution to the Argyros-Haydon question. We remark that all these spaces have finite dimensional Calkin algebra, and we investigate the corollaries of this result. We also construct a space with $ell_1$ Calkin algebra and show that whilst this space is still of Bourgain-Delbaen type with $ell_1$ dual, it behaves somewhat differently to the first class of spaces. Finally, we briefly consider shift-invariant $ell_1$ preduals, and hint at how one might use the Bourgain-Delbaen construction to produce new, exotic examples.

APA, Harvard, Vancouver, ISO, and other styles

25

Song, Hi Ja. "Gaussian measures on certain classes of Banach lattices /." The Ohio State University, 1985. http://rave.ohiolink.edu/etdc/view?acc_num=osu148726460321672.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Maergoiz, L., and Nikolai Tarkhanov. "Optimal recovery from a finite set in Banach spaces of entire functions." Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2009/3019/.

Full text

Abstract:

We develop an approach to the problem of optimal recovery of continuous linear functionals in Banach spaces through information on a finite number of given functionals. The results obtained are applied to the problem of the best analytic continuation from a finite set in the complex space Cn, n ≥ 1, for classes of entire functions of exponential type which belong to the space Lp, 1 < p < 1, on the real subspace of Cn. These latter are known as Wiener classes.

APA, Harvard, Vancouver, ISO, and other styles

27

Albasrawi, Fatimah Hassan. "Floquet Theory on Banach Space." TopSCHOLAR®, 2013. http://digitalcommons.wku.edu/theses/1234.

Full text

Abstract:

In this thesis we study Floquet theory on a Banach space. We are concerned about the linear differential equation of the form: y'(t) = A(t)y(t), where t ∈ R, y(t) is a function with values in a Banach space X, and A(t) are linear, bounded operators on X. If the system is periodic, meaning A(t+ω) = A(t) for some period ω, then it is called a Floquet system. We will investigate the existence and uniqueness of the periodic solution, as well as the stability of a Floquet system. This thesis will be presented in five main chapters. In the first chapter, we review the system of linear differential equations on Rn: y'= A(t)y(t) + f(t), where A(t) is an n x n matrix-valued function, y(t) are vectors and f(t) are functions with values in Rn. We establish the general form of the all solutions by using the fundamental matrix, consisting of n independent solutions. Also, we can find the stability of solutions directly by using the eigenvalues of A. In the second chapter, we study the Floquet system on Rn, where A(t+ω) = A(t). We establish the Floquet theorem, in which we show that the Floquet system is closely related to a linear system with constant coefficients, so the properties of those systems can be applied. In particular, we can answer the questions about the stability of the Floquet system. Then we generalize the Floquet theory to a linear system on Banach spaces. So we introduce to the readers Banach spaces in chapter three and the linear operators on Banach spaces in chapter four. In the fifth chapter we study the asymptotic properties of solutions of the system: y'(t) = A(t)y(t), where y(t) is a function with values in a Banach space X and A(t) are linear, bounded operators on X with A (t+ω) = A(t). For that system, we can show the evolution family U(t,s) representing the solutions is periodic, i.e. U(t+ω, s+ω) = U(t,s). Next we study the monodromy of the system V := U(ω,0). We point out that the spectrum set of V actually determines the stability of the Floquet system. Moreover, we show that the existence and uniqueness of the periodic solution of the nonhomogeneous equation in a Floquet system is equivalent to the fact that 1 belongs to the resolvent set of V.

APA, Harvard, Vancouver, ISO, and other styles

28

Krause, Cory A. "Infinitary Combinatorics and the Spreading Models of Banach Spaces." Thesis, University of North Texas, 2019. https://digital.library.unt.edu/ark:/67531/metadc1505210/.

Full text

Abstract:

Spreading models have become fundamental to the study of asymptotic geometry in Banach spaces. The existence of spreading models in every Banach space, and the so-called good sequences which generate them, was one of the first applications of Ramsey theory in Banach space theory. We use Ramsey theory and other techniques from infinitary combinatorics to examine some old and new questions concerning spreading models and good sequences. First, we consider the lp spreading model problem which asks whether a Banach space contains lp provided that every spreading model of a normalized block basic sequence of the basis is isometrically equivalent to lp. Next, using the Hindman-Milliken-Taylor theorem, we prove a new stabilization theorem for spreading models which produces a basic sequence all of whose normalized constant coefficient block basic sequences are good. When the resulting basic sequence is semi-normalized, all the spreading models generated by the above good sequences must be uniformly equivalent to lp or c0. Finally, we investigate the assumption that every normalized block tree on a Banach space has a good branch. This turns out to be a very strong assumption and is equivalent to the space being 1-asymptotic lp. We also show that the stronger assumption that every block basic sequence is good is equivalent to the space being stabilized 1-asymptotic lp.

APA, Harvard, Vancouver, ISO, and other styles

29

Hymel, Arthur J. (Arthur Joseph). "Weak and Norm Convergence of Sequences in Banach Spaces." Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc500521/.

Full text

Abstract:

We study weak convergence of sequences in Banach spaces. In particular, we compare the notions of weak and norm convergence. Although these modes of convergence usually differ, we show that in ℓ¹ they coincide. We then show a theorem of Rosenthal's which states that if {𝓍ₙ} is a bounded sequence in a Banach space, then {𝓍ₙ} has a subsequence {𝓍'ₙ} satisfying one of the following two mutually exclusive alternatives; (i) {𝓍'ₙ} is weakly Cauchy, or (ii) {𝓍'ₙ} is equivalent to the unit vector basis of ℓ¹.

APA, Harvard, Vancouver, ISO, and other styles

30

Kiteu, Marco M. "Orbits of operators on Hilbert space and some classes of Banach spaces." Kent State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=kent1341850621.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Brackebusch, Ruth Elaine. "James space on general trees /." The Ohio State University, 1985. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487260135357124.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Hare, David Edwin George. "A duality theory for Banach spaces with the Convex Point-of-Continuity Property." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/27313.

Full text

Abstract:

A norm ||⋅|| on a Banach space X is Fréchet differentiable at x ∈ X if there is a functional ∫∈ X* such that [Formula Omitted] This concept reflects the smoothness characteristics of X. A dual Banach space X* has the Radon-Nikodym Property (RNP) if whenever C ⊂ X* is weak*-compact and convex, and ∈ > 0, there is an x ∈ X and an ⍺ > 0 such that diameter [Formula Omitted] this property reflects the convexity characteristics of X*. Culminating several years of work by many researchers, the following theorem established a strong connection between the smoothness of X and the convexity of X*: Every equivalent norm on X is Fréchet differentiable on a dense set if and only if X* has the RNP. A more general measure of convexity has been recently receiving a great deal of attention: A dual Banach space X* has the weak* Convex Point-of-Continuity Property (C*PCP) if whenever ɸ ≠ C ⊂ X* is weak*-compact and convex, and ∈ > 0, there is a weak*-open set V such that V ⋂ C ≠ ɸ and diam V ⋂ C < ∈. In this thesis, we develop the corresponding smoothness properties of X which are dual to C*PCP. For this, a new type of differentiability, called cofinite Fréchet differentiability, is introduced, and we establish the following theorem: Every equivalent norm on X is cofinitely Fréchet differentiable everywhere if and only if X* has the C*PCP. Representing joint work with R. Deville, G. Godefroy and V. Zizler, an alternate approach is developed in the case when X is separable. We show that if X is separable, then every equivalent norm on X which has a strictly convex dual is Fréchet differentiable on a dense set if and only if X* has the C*PCP, if and only if every equivalent norm on X which is Gâteaux differentiable (everywhere) is Fréchet differentiable on a dense set. This result is used to show that if X* does not have the C*PCP, then there is a subspace Y of X such that neither Y* nor (X/Y)* have the C*PCP, yet both Y and X/Y have finite dimensional Schauder decompositions. The corresponding result for spaces X* failing the RNP remains open.<br>Science, Faculty of<br>Mathematics, Department of<br>Graduate

APA, Harvard, Vancouver, ISO, and other styles

33

Niyitegeka, Jean Marie Vianney. "Generalizations of some fixed point theorems in banach and metric spaces." Thesis, Nelson Mandela Metropolitan University, 2015. http://hdl.handle.net/10948/5265.

Full text

Abstract:

A fixed point of a mapping is an element in the domain of the mapping that is mapped into itself by the mapping. The study of fixed points has been a field of interests to mathematicians since the discovery of the Banach contraction theorem, i.e. if is a complete metric space and is a contraction mapping (i.e. there exists such that for all ), then has a unique fixed point. The Banach contraction theorem has found many applications in pure and applied mathematics. Due to fixed point theory being a mixture of analysis, geometry, algebra and topology, its applications to other fields such as physics, economics, game theory, chemistry, engineering and many others has become vital. The theory is nowadays a very active field of research in which many new theorems are published, some of them applied and many others generalized. Motivated by all of this, we give an exposition of some generalizations of fixed point theorems in metric fixed point theory, which is a branch of fixed point theory about results of fixed points of mappings between metric spaces, where certain properties of the mappings involved need not be preserved under equivalent metrics. For instance, the contractive property of mappings between metric spaces need not be preserved under equivalent metrics. Since metric fixed point theory is wide, we limit ourselves to fixed point theorems for self and non-self-mappings on Banach and metric spaces. We also take a look at some open problems on this topic of study. At the end of the dissertation, we suggest our own problems for future research.

APA, Harvard, Vancouver, ISO, and other styles

34

Lee, Haewon. "Nolinear Evolution Equations and Optimization Problems in Banach Spaces." Ohio University / OhioLINK, 2005. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1127498683.

Full text

APA, Harvard, Vancouver, ISO, and other styles

35

Crewe, Paul. "Some problems in abstract stochastic differential equations on Banach spaces." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:195c374f-3181-41b9-92d7-b375701a0b81.

Full text

Abstract:

This thesis studies abstract stochastic differential equations on Banach spaces. The well-posedness of abstract stochastic differential equations on such spaces is a recent result of van Neerven, Veraar and Weis, based on the theory of stochastic integration of Banach space valued processes constructed by the same authors. We study existence and uniqueness for solutions of stochastic differential equations with (possibly infinite) delay in their inputs on UMD Banach spaces. Such problems are also known as functional differential equations or delay differential equations. We show that the methods of van Neerven et al. extend to such problems if the initial history of the system lies in a space of a type introduced by Hale and Kato. The results are essentially of a fixed point type, both autonomous and non-autonomous cases are discussed and an example is given. We also study some long time properties of solutions to these stochastic differential equations on general Banach spaces. We show the existence of solutions to stochastic problems with almost periodicity in a weak or distributional sense. Results are again given for both autonomous and non-autonomous cases and depend heavily on estimates for R-bounds of operator families developed by Veraar. An example is given for a second order differential operator on a domain in ℝ<sup>d</sup>. Finally we consider the existence of invariant measures for such problems. This extends recent work of van Gaans in Hilbert spaces to Banach spaces of type 2.

APA, Harvard, Vancouver, ISO, and other styles

36

Chidume, Chukwudi Soares de Souza Geraldo. "Iteration methods for approximation of solutions of nonlinear equations in Banach spaces." Auburn, Ala., 2008. http://repo.lib.auburn.edu/EtdRoot/2008/SUMMER/Mathematics_and_Statistics/Dissertation/Chidume_Chukwudi_33.pdf.

Full text

APA, Harvard, Vancouver, ISO, and other styles

37

Bjorkman, Kaitlin. "A Weak Groethendieck Compactness Principle for Infinite Dimensional Banach Spaces." VCU Scholars Compass, 2013. http://scholarscompass.vcu.edu/etd/3042.

Full text

Abstract:

The goal of this thesis is to give an exposition of the following recent result of Freeman, Lennard, Odell, Turett and Randrianantoanina. A Banach space has the Schur property if and only if every weakly compact set is contained in the closed convex hull of a weakly null sequence. This result complements an old result of Grothendieck (now called the Grothendieck Compactness Principle) stating that every norm compact subset of a Banach space is contained in the closed convex hull of a norm null sequence. We include many of the relevant definitions and preliminary results which are required in the proofs of both of these theorems.

APA, Harvard, Vancouver, ISO, and other styles

38

Kozhushkina, Olena. "The Bishop-Phelps-Bollobás Theorem and Operators on Banach Spaces." Kent State University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=kent1404231789.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Robdera, Mangatiana A. "On the analytic complete continuity property of Banach spaces and convolution operators /." free to MU campus, to others for purchase, 1996. http://wwwlib.umi.com/cr/mo/fullcit?p9737875.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Alsulami, Saud M. A. "On Evolution Equations in Banach Spaces and Commuting Semigroups." Ohio University / OhioLINK, 2005. http://www.ohiolink.edu/etd/view.cgi?ohiou1126042587.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Braga, Bruno. "On the Borel complexity of some classes of Banach spaces." Kent State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=kent1377115201.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Schlackow, Iryna. "Classes of C(K) spaces with few operators." Thesis, University of Oxford, 2008. http://ora.ox.ac.uk/objects/uuid:e16273c8-c5fd-4a68-a9ca-cd4edb350c5c.

Full text

Abstract:

We investigate properties of Koszmider spaces. We show that if K and L are compact Hausdor spaces with no isolated points, K is Koszmider and C(K) is isomorphic to C(L), then K and L are homeomorphic and, in particular, L is also Koszmider. We also analyse topological properties of Koszmider spaces and show that a connected Koszmider space is strongly rigid. In addition to Koszmider spaces, we introduce the notion of weakly Koszmider spaces. Having established an alternative characterisation thereof, we show that, while it is evident that every Koszmider space is weakly Koszmider, the reverse implication does not hold. We also prove that if C(K) and C(L) are isomorphic and K is weakly Koszmider, then so is L. However, if K is Koszmider, there always exists a non-Koszmider space L such that C(K) and C(L) are isomorphic. In the second part of the thesis we present two separable Koszmider spaces the construction of which does not use any set-theoretical assumptions except for the usual (ZFC) axioms. The first space is zero-dimensional, being the Stone space of a Boolean algebra. The second construction results in a separable connected Koszmider space.

APA, Harvard, Vancouver, ISO, and other styles

43

Garcia, Francisco Javier. "THREE NON-LINEAR PROBLEMS ON NORMED SPACES." Kent State University / OhioLINK, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=kent1171042141.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Blower, G. "A topic in functional analysis." Thesis, University of Oxford, 1989. http://ora.ox.ac.uk/objects/uuid:0724199d-41fd-48f1-882c-19602576a2a0.

Full text

Abstract:

We introduce the class AUMD of Banach spaces X for which X-valued analytic martingales converge unconditionally. We shew that various possible definitions of this class are equivalent by methods of martingale decomposition. We shew that such X have finite cotype and are q-complex uniformly convex in the sense of Garling. Using multipliers we shew that analytic martingales valued in L<sup>1</sup> converge unconditionally and that AUMD spaces have the analytic Radon-Nikodym property. We shew that X has the AUMD property if and only if strong Hbrmander-Mihlin multipliers are bounded on the Hardy space H<sup>1</sup><sub>x</sub>(T). We achieve this by representing multipliers as martingale transforms. It is shewn that if X is in AUMD and is of cotype two then X has the Paley Theorem property. Using an isomorphism result we shew that if A is an injective operator system on a separable Hilbert space and P a completely bounded projection on A, then either PA or (I-P)A is completely boundedly isomorphic to A. The finite-dimensional version of this result is deduced from Ramsey's Theorem. It is shewn that B(e<sup>2</sup> is primary. It is shewn that weakly compact homomorphisms T from the 2 disc algebra into B(e<sup>2</sup> are necessarily compact. An explicit form for such T is obtained using spectral projections and it is deduced that such T are absolutely summing.

APA, Harvard, Vancouver, ISO, and other styles

45

Cho, Chong-Man d. "M-ideal structures in operator algebras /." The Ohio State University, 1985. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487259125219421.

Full text

APA, Harvard, Vancouver, ISO, and other styles

46

Ghaemi, Mohammad B. "Spectral theory of linear operators." Thesis, Connect to e-thesis, 2000. http://theses.gla.ac.uk/998/.

Full text

Abstract:

Thesis (Ph.D.) - University of Glasgow, 2000.<br>Ph.D. thesis submitted to the Department of Mathematics, University of Glasgow, 2000. Includes bibliographical references. Print version also available.

APA, Harvard, Vancouver, ISO, and other styles

47

De, Kock Mienie. "Absolute continuity and on the range of a vector measure." [Kent, Ohio] : Kent State University, 2008. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=kent1216134542.

Full text

Abstract:

Thesis (Ph.D.)--Kent State University, 2008.<br>Title from PDF t.p. (viewed Jan. 26, 2010). Advisor: Joseph Diestel. Keywords: absolute continiuty, range of a vector measure. Includes bibliographical references (p. 40-41).

APA, Harvard, Vancouver, ISO, and other styles

48

Constantin, Elena. "Optimization and flow invariance via high order tangent cones." Ohio : Ohio University, 2005. http://www.ohiolink.edu/etd/view.cgi?ohiou1125418579.

Full text

APA, Harvard, Vancouver, ISO, and other styles

49

Gimre, Karsten Trevor. "Quasi-local energy and isometric embedding." Thesis, 2016. https://doi.org/10.7916/D8765FB1.

Full text

Abstract:

In this thesis, we consider the recent definition of gravitational energy at the quasi-local level provided by Mu-Tao Wang and Shing-Tung Yau. Their definition poses a variational question predicated on isometric embedding of Riemannian surfaces into the Minkowski space; as such, there is a naturally associated Euler-Lagrange equation, which is a fourth-order system of partial differential equations for the embedding functions. We prove a perturbation result for solutions of this Euler-Lagrange equation.

APA, Harvard, Vancouver, ISO, and other styles

50

Lokesha, V. "Studies on theory of linear operators on Banach spaces." Thesis, 2002. http://hdl.handle.net/2009/1553.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!