Relevant bibliographies by topics / Normed linear spaces and Banach spaces

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Normed linear spaces and Banach spaces'

Author: Grafiati
Published: 4 June 2021
Last updated: 31 July 2024

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Journal articles on the topic "Normed linear spaces and Banach spaces"

1

Barnes, Benedict, I. A. Adjei, S. K. Amponsah, and E. Harris. "Product-Normed Linear Spaces." European Journal of Pure and Applied Mathematics 11, no. 3 (July 31, 2018): 740–50. http://dx.doi.org/10.29020/nybg.ejpam.v11i3.3284.

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In this paper, both the product-normed linear space $P-NLS$ (product-Banach space) and product-semi-normed linear space (product-semi-Banch space) are introduced. These normed linear spaces are endowed with the first and second product inequalities, which have a lot of applications in linear algebra and differential equations. In addition, we showed that $P-NLS$ admits functional properties such as completeness, continuity and the fixed point.
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2

Ettayb, J. "Some results on ultrametric 2-normed spaces." Researches in Mathematics 32, no. 1 (July 8, 2024): 45. http://dx.doi.org/10.15421/242404.

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In this paper, we study the ultrametric 2-normed spaces and the ultrametric 2-Banach spaces. In particular, we establish some results on Cauchy sequences in ultrametric 2-normed spaces. Also, we introduce and study the notion of bounded linear 2-functionals on ultrametric 2-Banach spaces and we give some of its properties. On the other hand, the new norm on the ultrametric 2-normed space is constructed. The concepts of closed operators between ultrametric 2-normed spaces and $b$-linear functionals in ultrametric 2-normed spaces are introduced. Finally, a necessary and sufficient condition for a linear operator to be closed in terms of its graph is proved and some results on bounded $b$-linear functionals in ultrametric 2-normed spaces are given.
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Narita, Keiko, Noboru Endou, and Yasunari Shidama. "Bidual Spaces and Reflexivity of Real Normed Spaces." Formalized Mathematics 22, no. 4 (December 1, 2014): 303–11. http://dx.doi.org/10.2478/forma-2014-0030.

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Summary In this article, we considered bidual spaces and reflexivity of real normed spaces. At first we proved some corollaries applying Hahn-Banach theorem and showed related theorems. In the second section, we proved the norm of dual spaces and defined the natural mapping, from real normed spaces to bidual spaces. We also proved some properties of this mapping. Next, we defined real normed space of R, real number spaces as real normed spaces and proved related theorems. We can regard linear functionals as linear operators by this definition. Accordingly we proved Uniform Boundedness Theorem for linear functionals using the theorem (5) from [21]. Finally, we defined reflexivity of real normed spaces and proved some theorems about isomorphism of linear operators. Using them, we proved some properties about reflexivity. These formalizations are based on [19], [20], [8] and [1].
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4

Bouadjila, K., A. Tallab, and E. Dahia. "Banach-Steinhaus theorem for linear relations on asymmetric normed spaces." Carpathian Mathematical Publications 14, no. 1 (June 30, 2022): 230–37. http://dx.doi.org/10.15330/cmp.14.1.230-237.

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We study the continuity of linear relations defined on asymmetric normed spaces with values in normed spaces. We give some geometric charactirization of these mappings. As an application, we prove the Banach-Steinhaus theorem in the framework of asymmetric normed spaces.
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Narita, Keiko, Noboru Endou, and Yasunari Shidama. "Dual Spaces and Hahn-Banach Theorem." Formalized Mathematics 22, no. 1 (March 30, 2014): 69–77. http://dx.doi.org/10.2478/forma-2014-0007.

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Summary In this article, we deal with dual spaces and the Hahn-Banach Theorem. At the first, we defined dual spaces of real linear spaces and proved related basic properties. Next, we defined dual spaces of real normed spaces. We formed the definitions based on dual spaces of real linear spaces. In addition, we proved properties of the norm about elements of dual spaces. For the proof we referred to descriptions in the article [21]. Finally, applying theorems of the second section, we proved the Hahn-Banach extension theorem in real normed spaces. We have used extensively used [17].
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6

Nakasho, Kazuhisa. "Bilinear Operators on Normed Linear Spaces." Formalized Mathematics 27, no. 1 (April 1, 2019): 15–23. http://dx.doi.org/10.2478/forma-2019-0002.

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Summary The main aim of this article is proving properties of bilinear operators on normed linear spaces formalized by means of Mizar [1]. In the first two chapters, algebraic structures [3] of bilinear operators on linear spaces are discussed. Especially, the space of bounded bilinear operators on normed linear spaces is developed here. In the third chapter, it is remarked that the algebraic structure of bounded bilinear operators to a certain Banach space also constitutes a Banach space. In the last chapter, the correspondence between the space of bilinear operators and the space of composition of linear opearators is shown. We referred to [4], [11], [2], [7] and [8] in this formalization.
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7

Alberto De Bernardi, Carlo, and Libor Veselý. "Tilings of Normed Spaces." Canadian Journal of Mathematics 69, no. 02 (April 2017): 321–37. http://dx.doi.org/10.4153/cjm-2015-057-3.

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Abstract By a tiling of a topological linear space X, we mean a covering of X by at least two closed convex sets, called tiles, whose nonempty interiors are pairwise disjoint. Study of tilings of infinite dimensional spaceswas initiated in the 1980's with pioneer papers by V. Klee. We prove some general properties of tilings of locally convex spaces, and then apply these results to study the existence of tilings of normed and Banach spaces by tiles possessing certain smoothness or rotundity properties. For a Banach space X, our main results are the following. (i) X admits no tiling by Fréchet smooth bounded tiles. (ii) If X is locally uniformly rotund (LUR), it does not admit any tiling by balls. (iii) On the other hand, some spaces, г uncountable, do admit a tiling by pairwise disjoint LUR bounded tiles.
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8

Gupta, Sahil, and T. D. Narang. "On strong proximinality in normed linear spaces." Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica 70, no. 1 (July 4, 2016): 19. http://dx.doi.org/10.17951/a.2016.70.1.19.

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The paper deals with strong proximinality in normed linear spaces. It is proved that in a compactly locally uniformly rotund Banach space, proximinality, strong proximinality, weak approximative compactness and approximative compactness are all equivalent for closed convex sets. How strong proximinality can be transmitted to and from quotient spaces has also been discussed.
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9

El-Shobaky, Entisarat, Sahar Mohammed Ali, and Wataru Takahashi. "On projection constant problems and the existence of metric projections in normed spaces." Abstract and Applied Analysis 6, no. 7 (2001): 401–11. http://dx.doi.org/10.1155/s1085337501000732.

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We give the sufficient conditions for the existence of a metric projection onto convex closed subsets of normed linear spaces which are reduced conditions than that in the case of reflexive Banach spaces and we find a general formula for the projections onto the maximal proper subspaces of the classical Banach spacesl p,1≤p<∞andc 0. We also give the sufficient and necessary conditions for an infinite matrix to represent a projection operator froml p,1≤p<∞orc 0onto anyone of their maximal proper subspaces.
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10

Nurnugroho, Burhanudin Arif, Supama Supama, and A. Zulijanto. "Operator Linear-2 Terbatas pada Ruang Bernorma-2 Non-Archimedean." Jurnal Fourier 8, no. 2 (October 31, 2019): 43–50. http://dx.doi.org/10.14421/fourier.2019.82.43-50.

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Di dalam paper ini dikonstruksikan operator linear-2 terbatas dari X2 ke Y , dengan X ruang bernorma-2 non-Archimedean dan ruang bernorma non-Archimedean. Di dalam paper ini ditunjukan bahwa himpunan semua operator linear-2 terbatas dari X2 to Y , ditulis B(X2, Y) merupakan ruang bernorma non-Archimedean. Selanjutnya, ditunjukan bahwa B(X2, Y), apabila Y ruang Banach non-Archimedean. [In this paper we construct bounded 2-linear operators from X2 to Y, where X is non-Archimedean 2-normed spaces and is a non-Archimedean-normed space. We prove that the set of all bounded 2-linear operators from X2 to Y , denoted by B(X2, Y) is a non-Archimedean normed spaces. Furthermore, we show that B(X2, Y) is a non-Archimedean Banach normed space, whenever Y is a non-Archimedean Banach space.]
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Dissertations / Theses on the topic "Normed linear spaces and Banach spaces"

1

Vuong, Thi Minh Thu. "Complemented and uncomplemented subspaces of Banach spaces." Thesis, University of Ballarat, 2006. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/51906.

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"A natural process in examining properties of Banach spaces is to see if a Banach space can be decomposed into simpler Banach spaces; in other words, to see if a Banach space has complemented subspaces. This thesis concentrates on three main aspects of this problem: norm of projections of a Banach space onto its finite dimensional subspaces; a class of Banach spaces, each of which has a large number of infinite dimensional complemented subspaces; and methods of finding Banach spaces which have uncomplemented subspaces, where the subspaces and the quotient spaces are chosen as well-known classical sequence spaces (finding non-trivial twisted sums)." --Abstract.
Master of Mathematical Sciences
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2

Vuong, Thi Minh Thu. "Complemented and uncomplemented subspaces of Banach spaces." University of Ballarat, 2006. http://archimedes.ballarat.edu.au:8080/vital/access/HandleResolver/1959.17/15540.

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"A natural process in examining properties of Banach spaces is to see if a Banach space can be decomposed into simpler Banach spaces; in other words, to see if a Banach space has complemented subspaces. This thesis concentrates on three main aspects of this problem: norm of projections of a Banach space onto its finite dimensional subspaces; a class of Banach spaces, each of which has a large number of infinite dimensional complemented subspaces; and methods of finding Banach spaces which have uncomplemented subspaces, where the subspaces and the quotient spaces are chosen as well-known classical sequence spaces (finding non-trivial twisted sums)." --Abstract.
Master of Mathematical Sciences
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3

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

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4

Vuong, Thi Minh Thu University of Ballarat. "Complemented and uncomplemented subspaces of Banach spaces." University of Ballarat, 2006. http://archimedes.ballarat.edu.au:8080/vital/access/HandleResolver/1959.17/12748.

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"A natural process in examining properties of Banach spaces is to see if a Banach space can be decomposed into simpler Banach spaces; in other words, to see if a Banach space has complemented subspaces. This thesis concentrates on three main aspects of this problem: norm of projections of a Banach space onto its finite dimensional subspaces; a class of Banach spaces, each of which has a large number of infinite dimensional complemented subspaces; and methods of finding Banach spaces which have uncomplemented subspaces, where the subspaces and the quotient spaces are chosen as well-known classical sequence spaces (finding non-trivial twisted sums)." --Abstract.
Master of Mathematical Sciences
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5

Baratov, Rishat. "Efficient conic decomposition and projection onto a cone in a Banach ordered space." Thesis, University of Ballarat, 2005. http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/61401.

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6

Tzschichholtz, Ingo. "Contributions to Lattice-like Properties on Ordered Normed Spaces." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2006. http://nbn-resolving.de/urn:nbn:de:swb:14-1153429885228-05773.

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Banachverbände spielen sowohl in der Theorie als auch in der Anwendung von geordneten normierten Räume eine bedeutende Rolle. Einerseits erweisen sich viele in der Praxis relevanten Räume als Banachverbände, andererseits ermöglichen die Vektorverbandsstruktur und die enge Beziehung zwischen Ordnung und Norm ein tiefes Verständnis solcher normierter Räume. An dieser Stelle setzen folgende Überlegungen an: - Die genaue Untersuchung einiger Resultate der reichhaltigen Banachverbandstheorie ließ (zu Recht) vermuten, dass in manchen Fällen die Verbandsnormeigenschaft keine notwendige Voraussetzung ist. In der Literatur gibt es bereits einige interessante Untersuchungen allgemeiner geordneter normierter Räume mit qualifizierten positiven Kegeln und in dem Zusammenhang eine Reihe wertvoller Dualitätsaussagen. An dieser Stelle sind die Eigenschaften der Normalität, der Nichtabgeflachtheit und der Regularität eines Kegels erwähnt, welche selbst im Falle eines mit einer Norm versehenen Vektorverbandes eine schwächere Relation zwischen Ordnung und Norm ergeben als die Verbandsnormeigenschaft. - In einer neueren Arbeit wurde der aus der Theorie der Vektorverbände gut bekannte Begriff der Disjunktheit bereits auf beliebige geordnete Räume verallgemeinert, wobei viele Eigenschaften disjunkter Vektoren, des disjunkten Komplements einer Menge usw., welche aus der Verbandstheorie bekannt sind, erhalten bleiben. Auf entsprechende Weise, d.h. durch das Ersetzen exakter Infima und Suprema durch Mengen unterer bzw. oberer Schranken, können der Modul eines Vektors sowie der Begriff der Solidität einer Menge für geordnete (normierte) Räume eingeführt werden. An solchen Überlegungen knüpft die vorliegende Arbeit an. Im Kapitel m-Normen ======== werden verallgemeinerte Formen der M-Norm Eigenschaft eingeführt und untersucht. AM-Räume und (approximative) Ordnungseinheit-Räume sind Beispiele für geordnete normierte Räume mit m-Norm. Die Schwerpunkte dieses Kapitels sind zum Einen Kegel- und Normeigenschaften dieser Räume und deren Charakterisierung mit Hilfe solcher Eigenschaften und zum Anderen Dualitätsaussagen, wie sie zum Teil bereits aus der Theorie der AM- und AL-Räume bekannt sind. Minimal totale Mengen ===================== Ziel dieses Kapitels ist es, den oben erwähnten verallgemeinerten Disjunktheitsbegiff für geordnete normierte Räume zu untersuchen. Eine zentrale Rolle spielen dabei totale Mengen im Dualraum und insbesondere minimal totale Mengen sowie deren Zusammenhang mit der Disjunktheit von Elementen des Ausgangsraumes. Normierte pre-Riesz Räume ========================= Wie bereits bekannt, lässt sich jeder pre-Riesz Raum ordnungsdicht in einen (bis auf Isomorphie) eindeutigen minimalen Vektorverband einbetten, die so genannte Riesz Vervollständigung. Ist der pre-Riesz Raum normiert und sein positiver Kegel abgeschlossen, dann kann eine Verbandsnorm auf der Riesz Vervollständigung eingeführt werden, welche sich in vielen Fällen als äquivalent zur Ausgangsnorm auf dem pre-Riesz Raum erweist. Es ist allgemein bekannt, dass sich dann auch stetige lineare Funktionale fortsetzen lassen. In diesem Kapitel wird nun untersucht, inwiefern sich Ordnungsrelationen auf einer Menge stetiger linearer Funktionale beim Übergang zur Menge der Fortsetzungen erhalten lassen. Die gewonnenen Erkenntnisse kommen anschließend bei Untersuchungen zur schwachen bzw. schwach*-Topologie auf geordneten normierten Räumen zur Anwendung. Hierbei werden zwei Fragestellungen behandelt. Zum Einen gilt das Augenmerk disjunkten Folgen in geordneten normierten Räumen. Als Beispiel seien ordnungsbeschränkte disjunkte Folgen in geordneten normierten Räumen mit halbmonotoner mNorm genannt, welche stets schwach gegen Null konvergieren. Zum Anderen werden monoton fallende Folgen und Netze bzw. disjunkte Folgen von stetigen linearen Funktionalen auf einem geordneten normierten Raum betrachtet
Banach lattices play an important role in the theory of ordered normed spaces. One reason is, that many ordered normed vector spaces, that are important in practice, turn out to be Banach lattices, on the other hand, the lattice structure and strong relations between order and norm allow a deep understanding of such ordered normed spaces. At this point the following is to be considered. - The analysis of some results in the rich Banach lattice theory leads to the conjecture, that sometimes the lattice norm property is no necessary supposition. General ordered normed spaces with a convenient positive cone were already examined, where some valuable duality properties could be achieved. We point out the properties of normality, non-flatness and regularity of a cone, which are a weaker relation between order and norm than the lattice norm property in normed vector lattices. - The notion of disjointness in vector lattices has already been generalized to arbitrary ordered vector spaces. Many properties of disjoint elements, the disjoint complement of a set etc., well known from the vector lattice theory, are preserved. The modulus of a vector as well as the concept of the solidness of a set can be introduced in a similar way, namely by replacing suprema and infima by sets of upper and lower bounds, respectively. We take such ideas up in the present thesis. A generalized version of the M-norm property is introduced and examined in section m-norms. ======= AM-spaces and approximate order unit spaces are examples of ordered normed spaces with m-norm. The main points of this section are the special properties of the positive cone and the norm of such spaces and the duality properties of spaces with m-norm. Minimal total sets ================== In this section we examine the mentioned generalized disjointness in ordered normed spaces. Total sets as well as minimal total sets and their relation to disjoint elements play an inportant at this. Normed pre-Riesz spaces ======================= As already known, every pre-Riesz space can be order densely embedded into an (up to isomorphism) unique vector lattice, the so called Riesz completion. If, in addition, the pre-Riesz space is normed and its positive cone is closed, then a lattice norm can be introduced on the Riesz completion, that turns out to be equivalent to the primary norm on the pre-Riesz space in many cases. Positive linear continuous functionals on the pre-Riesz space are extendable to positive linear continuous functionals in this setting. Here we investigate, how some order relations on a set of continuous functionals can be preserved to the set of the extension. In the last paragraph of this section the obtained results are applied for investigations of some questions concerning the weak and the weak* topology on ordered normed vector spaces. On the one hand, we focus on disjoint sequences in ordered normed spaces. On the other hand, we deal with decreasing sequences and nets and disjoint sequences of linear continuous functionals on ordered normed spaces
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7

Tzschichholtz, Ingo. "Contributions to Lattice-like Properties on Ordered Normed Spaces." Doctoral thesis, Technische Universität Dresden, 2005. https://tud.qucosa.de/id/qucosa%3A24878.

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Banachverbände spielen sowohl in der Theorie als auch in der Anwendung von geordneten normierten Räume eine bedeutende Rolle. Einerseits erweisen sich viele in der Praxis relevanten Räume als Banachverbände, andererseits ermöglichen die Vektorverbandsstruktur und die enge Beziehung zwischen Ordnung und Norm ein tiefes Verständnis solcher normierter Räume. An dieser Stelle setzen folgende Überlegungen an: - Die genaue Untersuchung einiger Resultate der reichhaltigen Banachverbandstheorie ließ (zu Recht) vermuten, dass in manchen Fällen die Verbandsnormeigenschaft keine notwendige Voraussetzung ist. In der Literatur gibt es bereits einige interessante Untersuchungen allgemeiner geordneter normierter Räume mit qualifizierten positiven Kegeln und in dem Zusammenhang eine Reihe wertvoller Dualitätsaussagen. An dieser Stelle sind die Eigenschaften der Normalität, der Nichtabgeflachtheit und der Regularität eines Kegels erwähnt, welche selbst im Falle eines mit einer Norm versehenen Vektorverbandes eine schwächere Relation zwischen Ordnung und Norm ergeben als die Verbandsnormeigenschaft. - In einer neueren Arbeit wurde der aus der Theorie der Vektorverbände gut bekannte Begriff der Disjunktheit bereits auf beliebige geordnete Räume verallgemeinert, wobei viele Eigenschaften disjunkter Vektoren, des disjunkten Komplements einer Menge usw., welche aus der Verbandstheorie bekannt sind, erhalten bleiben. Auf entsprechende Weise, d.h. durch das Ersetzen exakter Infima und Suprema durch Mengen unterer bzw. oberer Schranken, können der Modul eines Vektors sowie der Begriff der Solidität einer Menge für geordnete (normierte) Räume eingeführt werden. An solchen Überlegungen knüpft die vorliegende Arbeit an. Im Kapitel m-Normen ======== werden verallgemeinerte Formen der M-Norm Eigenschaft eingeführt und untersucht. AM-Räume und (approximative) Ordnungseinheit-Räume sind Beispiele für geordnete normierte Räume mit m-Norm. Die Schwerpunkte dieses Kapitels sind zum Einen Kegel- und Normeigenschaften dieser Räume und deren Charakterisierung mit Hilfe solcher Eigenschaften und zum Anderen Dualitätsaussagen, wie sie zum Teil bereits aus der Theorie der AM- und AL-Räume bekannt sind. Minimal totale Mengen ===================== Ziel dieses Kapitels ist es, den oben erwähnten verallgemeinerten Disjunktheitsbegiff für geordnete normierte Räume zu untersuchen. Eine zentrale Rolle spielen dabei totale Mengen im Dualraum und insbesondere minimal totale Mengen sowie deren Zusammenhang mit der Disjunktheit von Elementen des Ausgangsraumes. Normierte pre-Riesz Räume ========================= Wie bereits bekannt, lässt sich jeder pre-Riesz Raum ordnungsdicht in einen (bis auf Isomorphie) eindeutigen minimalen Vektorverband einbetten, die so genannte Riesz Vervollständigung. Ist der pre-Riesz Raum normiert und sein positiver Kegel abgeschlossen, dann kann eine Verbandsnorm auf der Riesz Vervollständigung eingeführt werden, welche sich in vielen Fällen als äquivalent zur Ausgangsnorm auf dem pre-Riesz Raum erweist. Es ist allgemein bekannt, dass sich dann auch stetige lineare Funktionale fortsetzen lassen. In diesem Kapitel wird nun untersucht, inwiefern sich Ordnungsrelationen auf einer Menge stetiger linearer Funktionale beim Übergang zur Menge der Fortsetzungen erhalten lassen. Die gewonnenen Erkenntnisse kommen anschließend bei Untersuchungen zur schwachen bzw. schwach*-Topologie auf geordneten normierten Räumen zur Anwendung. Hierbei werden zwei Fragestellungen behandelt. Zum Einen gilt das Augenmerk disjunkten Folgen in geordneten normierten Räumen. Als Beispiel seien ordnungsbeschränkte disjunkte Folgen in geordneten normierten Räumen mit halbmonotoner mNorm genannt, welche stets schwach gegen Null konvergieren. Zum Anderen werden monoton fallende Folgen und Netze bzw. disjunkte Folgen von stetigen linearen Funktionalen auf einem geordneten normierten Raum betrachtet.
Banach lattices play an important role in the theory of ordered normed spaces. One reason is, that many ordered normed vector spaces, that are important in practice, turn out to be Banach lattices, on the other hand, the lattice structure and strong relations between order and norm allow a deep understanding of such ordered normed spaces. At this point the following is to be considered. - The analysis of some results in the rich Banach lattice theory leads to the conjecture, that sometimes the lattice norm property is no necessary supposition. General ordered normed spaces with a convenient positive cone were already examined, where some valuable duality properties could be achieved. We point out the properties of normality, non-flatness and regularity of a cone, which are a weaker relation between order and norm than the lattice norm property in normed vector lattices. - The notion of disjointness in vector lattices has already been generalized to arbitrary ordered vector spaces. Many properties of disjoint elements, the disjoint complement of a set etc., well known from the vector lattice theory, are preserved. The modulus of a vector as well as the concept of the solidness of a set can be introduced in a similar way, namely by replacing suprema and infima by sets of upper and lower bounds, respectively. We take such ideas up in the present thesis. A generalized version of the M-norm property is introduced and examined in section m-norms. ======= AM-spaces and approximate order unit spaces are examples of ordered normed spaces with m-norm. The main points of this section are the special properties of the positive cone and the norm of such spaces and the duality properties of spaces with m-norm. Minimal total sets ================== In this section we examine the mentioned generalized disjointness in ordered normed spaces. Total sets as well as minimal total sets and their relation to disjoint elements play an inportant at this. Normed pre-Riesz spaces ======================= As already known, every pre-Riesz space can be order densely embedded into an (up to isomorphism) unique vector lattice, the so called Riesz completion. If, in addition, the pre-Riesz space is normed and its positive cone is closed, then a lattice norm can be introduced on the Riesz completion, that turns out to be equivalent to the primary norm on the pre-Riesz space in many cases. Positive linear continuous functionals on the pre-Riesz space are extendable to positive linear continuous functionals in this setting. Here we investigate, how some order relations on a set of continuous functionals can be preserved to the set of the extension. In the last paragraph of this section the obtained results are applied for investigations of some questions concerning the weak and the weak* topology on ordered normed vector spaces. On the one hand, we focus on disjoint sequences in ordered normed spaces. On the other hand, we deal with decreasing sequences and nets and disjoint sequences of linear continuous functionals on ordered normed spaces.
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8

Johnson, Solomon Nathan. "Best simultaneous approximation in normed linear spaces." Thesis, Rhodes University, 2018. http://hdl.handle.net/10962/58985.

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In this thesis we consider the problem of simultaneously approximating elements of a set B C X by a single element of a set K C X. This type of a problem arises when the element to be approximated is not known precisely but is known to belong to a set.Thus, best simultaneous approximation is a natural generalization of best approximation which has been studied extensively. The theory of best simultaneous approximation has been studied by many authors, see for example [4], [8], [25], [28], [26] and [12] to name but a few.
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9

Wilcox, Diane. "Multivalued semi-Fredholm operators in normed linear spaces." Doctoral thesis, University of Cape Town, 2002. http://hdl.handle.net/11427/4945.

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Bibliography: leaves 176-182.
Certain properties associated with these classes are stable under small perturbation, i.e. stable under additive perturbation by continuous operators whose norms are less than the minimum modulus of the relation being perturbed, and are also stable under perturbation by compact, strictly singular or strictly cosingular operators. In this work we continue the study of these classes and introduce the classes of α-Atkinson and β-Atkinson relations. These are subclasses of upper and lower semi-Fredholm relations respectively, having generalised inverses and defined in terms of the existence of continuous projections onto their ranges and nullspaces.
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Ameur, Yacin. "Interpolation of Hilbert spaces /." Uppsala : Matematiska institutionen, Univ. [distributör], 2001. http://publications.uu.se/theses/91-506-1531-9/.

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Books on the topic "Normed linear spaces and Banach spaces"

1

Michal, Johanis, ed. Smooth analysis in Banach spaces. Berlin: De Gruyter, 2014.

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2

Deville, R. Smoothness and renormings in Banach spaces. Harlow, Essex, England: Longman Scientific & Technical, 1993.

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Deville, Robert. Smoothness and renormings in Banach spaces. Harlow: Longman Scientific and Technical, 1993.

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Verheul, E. R. Multimedians in metric and normed spaces. Amsterdam, the Netherlands: Centrum voor Wiskunde en Informatica, 1993.

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Bennett, Grahame. Factorizing the classical inequalities. Providence, R.I: American Mathematical Society, 1996.

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Conference on Function Spaces (7th 2014 Southern Illinois University at Edwardsville). Function spaces in analysis: 7th Conference on Function Spaces, May 20-24, 2014, Southern Illinois University, Edwardsville, Illinois. Edited by Jarosz Krzysztof 1953 editor. Providence, Rhode Island: American Mathematical Society, 2015.

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1963-, Giannopoulos Apostolos, and Milman Vitali D. 1939-, eds. Asymptotic geometric analysis. Providence, Rhode Island: American Mathematical Society, 2015.

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Krzysztof, Jarosz, ed. Function spaces in modern analysis: Sixth Conference on Function Spaces, May 18-22, 2010, Southern Illinois University, Edwardsville. Providence, R.I: American Mathematical Society, 2011.

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Haydon, R. Randomly normed spaces. Paris: Hermann Editeurs des Sciences et des Arts, 1991.

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Guillén, Bernardo Lafuerza. Probabilistic normed spaces. Hackensack, NJ: Imperial College Press, 2014.

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Book chapters on the topic "Normed linear spaces and Banach spaces"

1

Browder, Felix E. "Normal Solvability And Existence Theorems For Nonlinear Mappings In Banach Spaces." In Problems in Non-Linear Analysis, 17–35. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-10998-0_2.

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Browder, Felix E. "Normal Solvability for Nonlinear Mappings and the Geometry of Banach Spaces." In Problems in Non-Linear Analysis, 37–66. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-10998-0_3.

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Guirao, Antonio José, Vicente Montesinos, and Václav Zizler. "Norms, normed spaces, Banach spaces." In Renormings in Banach Spaces, 3–14. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-08655-7_1.

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Kress, Rainer. "Normed Spaces." In Linear Integral Equations, 1–14. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-0559-3_1.

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Kress, Rainer. "Normed Spaces." In Linear Integral Equations, 1–12. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-97146-4_1.

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Cheney, Ward. "Normed Linear Spaces." In Graduate Texts in Mathematics, 1–60. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4757-3559-8_1.

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Kesavan, S. "Normed Linear Spaces." In Functional Analysis, 26–68. Gurgaon: Hindustan Book Agency, 2009. http://dx.doi.org/10.1007/978-93-86279-42-2_2.

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Bishop, Errett, and Douglas Bridges. "Normed Linear Spaces." In Grundlehren der mathematischen Wissenschaften, 299–398. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-61667-9_8.

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Bartle, Robert. "Normed linear spaces." In Graduate Studies in Mathematics, 401–11. Providence, Rhode Island: American Mathematical Society, 2001. http://dx.doi.org/10.1090/gsm/032/29.

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Dym, Harry. "Normed linear spaces." In Graduate Studies in Mathematics, 133–60. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/gsm/078/07.

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Conference papers on the topic "Normed linear spaces and Banach spaces"

1

Balamurugan, J., and B. Baskaran. "Characterization of 2-normed linear spaces." In 2ND INTERNATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND APPLICATIONS: ICMTA2021. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0109159.

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Stringa, Artur. "On Uniformly Convex Linear 2 – Normed Spaces." In The 6th International Virtual Conference on Advanced Scientific Results. Publishing Society, 2018. http://dx.doi.org/10.18638/scieconf.2018.6.1.485.

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Wen Li, Du Zou, Deyi Li, and Zhaoyuan Zhang. "Best approximation in asymmetric normed linear spaces." In 2011 International Conference on Information Science and Technology (ICIST). IEEE, 2011. http://dx.doi.org/10.1109/icist.2011.5765276.

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Acikgoz, Mehmet, Yusuf Karakus, Nurgul Aslan, Nurten Koskeroglu, Serkan Araci, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Apollonious Identity in Linear 2-Normed Spaces." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP, 2009. http://dx.doi.org/10.1063/1.3241419.

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Muradov, Firudin Kh. "On the continuous linear maps of real normed spaces." In 10TH INTERNATIONAL CONFERENCE ON APPLIED SCIENCE AND TECHNOLOGY. AIP Publishing, 2022. http://dx.doi.org/10.1063/5.0115341.

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Oprea, Ramona Ioana, Pater Flavius, Adina Juratoni, and Olivia Bundau. "An introduction to spectral theory in fuzzy normed linear spaces." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0026609.

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Aiena, Pietro. "Weyl type theorems for bounded linear operators on Banach spaces." In Proceedings of the Fourth International School — In Memory of Professor Antonio Aizpuru Tomás. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814335812_0002.

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Szabo, Alexandru, Tudor Bînzar, Sorin Nădăban, and Flavius Pater. "Some properties of fuzzy bounded sets in fuzzy normed linear spaces." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5043993.

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Liu Lixin. "Exponential stability of quasi-linear non-autonomous differential equations in Banach spaces." In 2008 Chinese Control Conference (CCC). IEEE, 2008. http://dx.doi.org/10.1109/chicc.2008.4605484.

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Boulite, S., S. Hadd, H. Nounou, and M. Nounou. "The PI-Controller for infinite dimensional linear systems in Banach state spaces." In 2009 American Control Conference. IEEE, 2009. http://dx.doi.org/10.1109/acc.2009.5160573.

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