Relevant bibliographies by topics / Banach spaces Linear operators Spectral theory (Mathematics)

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  2. Dissertations / Theses
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Academic literature on the topic 'Banach spaces Linear operators Spectral theory (Mathematics)'

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Published: 4 June 2021
Last updated: 2 February 2022

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Journal articles on the topic "Banach spaces Linear operators Spectral theory (Mathematics)"

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ZENG, QINGPING. "Five short lemmas in Banach spaces." Carpathian Journal of Mathematics 32, no. 1 (2016): 131–40. http://dx.doi.org/10.37193/cjm.2016.01.14.

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Consider a commutative diagram of bounded linear operators between Banach spaces...with exact rows. In what ways are the spectral and local spectral properties of B related to those of the pairs of operators A and C? In this paper, we give our answers to this general question using tools from local spectral theory.
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Ricker, W. "Spectral operators and weakly compact homomorphisms in a class of Banach Spaces." Glasgow Mathematical Journal 28, no. 2 (July 1986): 215–22. http://dx.doi.org/10.1017/s0017089500006534.

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The purpose of this note is to present certain aspects of the theory of spectral operators in Grothendieck spaces with the Dunford-Pettis property, briefly, GDP-spaces, thereby elaborating on the recent note [10].For example, the sum and product of commuting spectral operators in such spaces are again spectral operators (cf. Proposition 2.1) and a continuous linear operator is spectral if and only if it has finite spectrum (cf. Proposition 2.2). Accordingly, if a spectral operator is of finite type, then its spectrum consists entirely of eigenvalues. Furthermore, it turns out that there are no unbounded spectral operators in such spaces (cf. Proposition 2.4). As a simple application of these results we are able to determine which multiplication operators in certain function spaces are spectral operators.
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Laursen, Kjeld B., and Michael M. Neumann. "Local spectral theory and spectral inclusions." Glasgow Mathematical Journal 36, no. 3 (September 1994): 331–43. http://dx.doi.org/10.1017/s0017089500030937.

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Suppose that T and S are continuous linear operators on complex Banach spaces X and Y, respectively, and that A is a non-zero continuous linear mapping from X to Y. If A intertwines T and S in the sense that SA = AT, then a classical result due to Rosenblum implies that the spectra σ(T) and σ(S) must overlap, see [12]. Actually, Davis and Rosenthal [5]have shown that the surjectivity spectrum σsu(T) will meet the approximate point spectrum σap(S) in this case (terms to be denned below). Further information about the relations between the two spectra and their finer structure becomes available when the intertwiner A is injective or has dense range, see [9], [12], [13].
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Laursen, Kjeld B., Vivien G. Miller, and Michael M. Neumann. "Local spectral properties of commutators." Proceedings of the Edinburgh Mathematical Society 38, no. 2 (June 1995): 313–29. http://dx.doi.org/10.1017/s0013091500019106.

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For a pair of continuous linear operators T and S on complex Banach spaces X and Y, respectively, this paper studies the local spectral properties of the commutator C(S, T) given by C(S, T)(A): = SA−AT for all A∈L(X, Y). Under suitable conditions on T and S, the main results provide the single valued extension property, a description of the local spectrum, and a characterization of the spectral subspaces of C(S, T), which encompasses the closedness of these subspaces. The strongest results are obtained for quotients and restrictions of decomposable operators. The theory is based on the recent characterization of such operators by Albrecht and Eschmeier and extends the classical results for decomposable operators due to Colojoară, Foiaş, and Vasilescu to considerably larger classes of operators. Counterexamples from the theory of semishifts are included to illustrate that the assumptions are appropriate. Finally, it is shown that the commutator of two super-decomposable operators is decomposable.
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Tahir, Jawad Kadhim. "Numerical Computations for One Class of Dynamical Mathematical Models in Quasi-Sobolev Space." Mathematical Modelling of Engineering Problems 8, no. 2 (April 28, 2021): 267–72. http://dx.doi.org/10.18280/mmep.080214.

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The article studies some mathematical models that represent one class of dynamical equations in quasi-Sobolev space. The analytical investigation of solvability of the Cauchy problem in the quasi-Sobolev space and theoretical results used to enhance and develop an algorithm structure of the numerical procedures to find approximate solutions for models, the steps of algorithm based on the theoretical investigation of models, new algorithm of numerical method allowing to find approximate solutions of mathematical models under study in quasi-Sobolev space. Construction a program implements an algorithm of numerical method that allow finding approximate solutions for models. To construct the theory of degenerate holomorphic semigroups of operators in quasi-Banach spaces of sequences, we used the classical methods of functional analysis, theory of linear bounded operators, spectral theory. To construct the operators of resolving semigroups we used the Laplace transform of operator-valued functions in quasi-Banach spaces of sequences. The numerical investigation for models generate some approximate solutions which are normally based on the modified projection method. The convergence of the approximate solution to the exact one theoretically is justified by the convergence of the corresponding series, the agreement of approximate computations with the theoretical solution is established.
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Ludkovsky, S., and B. Diarra. "Spectral integration and spectral theory for non-Archimedean Banach spaces." International Journal of Mathematics and Mathematical Sciences 31, no. 7 (2002): 421–42. http://dx.doi.org/10.1155/s016117120201150x.

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Banach algebras over arbitrary complete non-Archimedean fields are considered such that operators may be nonanalytic. There are different types of Banach spaces over non-Archimedean fields. We have determined the spectrum of some closed commutative subalgebras of the Banach algebraℒ(E)of the continuous linear operators on a free Banach spaceEgenerated by projectors. We investigate the spectral integration of non-Archimedean Banach algebras. We define a spectral measure and prove several properties. We prove the non-Archimedean analog of Stone theorem. It also contains the case ofC-algebrasC∞(X,𝕂). We prove a particular case of a representation of aC-algebra with the help of aL(Aˆ,μ,𝕂)-projection-valued measure. We consider spectral theorems for operators and families of commuting linear continuous operators on the non-Archimedean Banach space.
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Edmunds, D. E., W. D. Evans, and D. J. Harris. "A spectral analysis of compact linear operators in Banach spaces." Bulletin of the London Mathematical Society 42, no. 4 (May 17, 2010): 726–34. http://dx.doi.org/10.1112/blms/bdq030.

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Baskakov, A. G., and A. S. Zagorskii. "Spectral theory of linear relations on real Banach spaces." Mathematical Notes 81, no. 1-2 (February 2007): 15–27. http://dx.doi.org/10.1134/s0001434607010026.

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Zguitti, Hassane. "A note on the common spectral properties for bounded linear operators." Filomat 33, no. 14 (2019): 4575–84. http://dx.doi.org/10.2298/fil1914575z.

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Let X and Y be Banach spaces, A : X ? Y and B, C : Y ? X be bounded linear operators. We prove that if A(BA)2 = ABACA = ACABA = (AC)2A, then ?*(AC) {0} = ?*(BA)\{0} where ?+ runs over a large of spectra originated by regularities.
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Roman, Marcel, and Adrian Sandovici. "$B$-spectral theory of linear relations in complex Banach spaces." Publicationes Mathematicae Debrecen 91, no. 3-4 (October 1, 2017): 455–66. http://dx.doi.org/10.5486/pmd.2017.7781.

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Dissertations / Theses on the topic "Banach spaces Linear operators Spectral theory (Mathematics)"

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

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Thesis (Ph.D.) - University of Glasgow, 2000.
Ph.D. thesis submitted to the Department of Mathematics, University of Glasgow, 2000. Includes bibliographical references. Print version also available.
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Albasrawi, Fatimah Hassan. "Floquet Theory on Banach Space." TopSCHOLAR®, 2013. http://digitalcommons.wku.edu/theses/1234.

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

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Vermaak, Jacobus Andries. "Riesz- en Fredholmteorie in Banach-algebras." Thesis, 2014. http://hdl.handle.net/10210/12031.

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Books on the topic "Banach spaces Linear operators Spectral theory (Mathematics)"

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Erdelyi, Ivan. A local spectral theory for closed operators. Cambridge: Cambridge University Press, 1986.

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1932-, Wang Shengwang, ed. A local spectral theory for closed operators. Cambridge [Cambridgeshire]: Cambridge University Press, 1985.

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Simon, Barry. Operator theory. Providence, Rhode Island: American Mathematical Society, 2015.

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Orlik, Lyubov', and Galina Zhukova. Operator equation and related questions of stability of differential equations. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1061676.

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The monograph is devoted to the application of methods of functional analysis to the problems of qualitative theory of differential equations. Describes an algorithm to bring the differential boundary value problem to an operator equation. The research of solutions to operator equations of special kind in the spaces polutoratonny with a cone, where the limitations of the elements of these spaces is understood as the comparability them with a fixed scale element of exponential type. Found representations of the solutions of operator equations in the form of contour integrals, theorems of existence and uniqueness of such solutions. The spectral criteria for boundedness of solutions of operator equations and, as a consequence, sufficient spectral features boundedness of solutions of differential and differential-difference equations in Banach space. The results obtained for operator equations with operators and work of Volterra operators, allowed to extend to some systems of partial differential equations known spectral stability criteria for solutions of A. M. Lyapunov and also to generalize theorems on the exponential characteristic. The results of the monograph may be useful in the study of linear mechanical and electrical systems, in problems of diffraction of electromagnetic waves, theory of automatic control, etc. It is intended for researchers, graduate students functional analysis and its applications to operator and differential equations.
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Edmunds, David, and Des Evans. Spectral Theory and Differential Operators. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.001.0001.

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This book gives an account of those parts of the analysis of closed linear operators acting in Banach or Hilbert spaces that are relevant to spectral problems involving differential operators, and makes applications to such questions. After the exposition of the abstract theory in the first four chapters, Sobolev spaces are introduced and their main properties established. The remaining seven chapters are largely concerned with second-order elliptic differential operators and related boundary-value problems. Particular attention is paid to the spectrum of the Schrödinger operator. Its original form contains material of lasting importance that is relatively unaffected by advances in the theory since 1987, when the book was first published. The present edition differs from the old by virtue of the correction of minor errors and improvements of various proofs. In addition, it contains Notes at the ends of most chapters, intended to give the reader some idea of recent developments together with additional references that enable more detailed accounts to be accessed.
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Book chapters on the topic "Banach spaces Linear operators Spectral theory (Mathematics)"

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Edmunds, D. E., W. D. Evans, and D. J. Harris. "Representations of Compact Linear Operators in Banach Spaces and Nonlinear Eigenvalue Problems II." In Spectral Theory and Analysis, 21–37. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-7643-9994-8_2.

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Boules, Adel N. "Banach Spaces." In Fundamentals of Mathematical Analysis, 245–89. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780198868781.003.0006.

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The first four sections of this chapter form its core and include classical topics such as bounded linear transformations, the open mapping theorem, the closed graph theorem, the uniform boundedness principle, and the Hahn-Banach theorem. The chapter includes a good number of applications of the four fundamental theorems of functional analysis. Sections 6.5 and 6.6 provide a good account of the properties of the spectrum and adjoint operators on Banach spaces. They may be largely bypassed, since the treatment of the corresponding topics for operators on Hilbert spaces in chapter 7 is self-contained. The section on weak topologies is more advanced and may be omitted if a brief introduction is the goal. The chapter is enriched by such topics as the best polynomial approximation, the Hilbert cube, Gelfand’s theorem, Schauder bases, complemented subspaces, and the Banach-Alaoglu theorem.
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