counterexamples in topological vector spaces lecture notes in mathematics

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Counterexamples In Topological Vector Spaces

Author : S.M. Khaleelulla
ISBN : 9783540392682
Genre : Mathematics
File Size : 76. 84 MB
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Semitopological Vector Spaces

Author : Mark Burgin
ISBN : 9781771885355
Genre : Mathematics
File Size : 40. 57 MB
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This new volume shows how it is possible to further develop and essentially extend the theory of operators in infinite-dimensional vector spaces, which plays an important role in mathematics, physics, information theory, and control theory. The book describes new mathematical structures, such as hypernorms, hyperseminorms, hypermetrics, semitopological vector spaces, hypernormed vector spaces, and hyperseminormed vector spaces. It develops mathematical tools for the further development of functional analysis and broadening of its applications. Exploration of semitopological vector spaces, hypernormed vector spaces, hyperseminormed vector spaces, and hypermetric vector spaces is the main topic of this book. A new direction in functional analysis, called quantum functional analysis, has been developed based on polinormed and multinormed vector spaces and linear algebras. At the same time, normed vector spaces and topological vector spaces play an important role in physics and in control theory. To make this book comprehendible for the reader and more suitable for students with some basic knowledge in mathematics, denotations and definitions of the main mathematical concepts and structures used in the book are included in the appendix, making the book useful for enhancing traditional courses of calculus for undergraduates, as well as for separate courses for graduate students. The material of Semitopological Vector Spaces: Hypernorms, Hyperseminorms and Operators is closely related to what is taught at colleges and universities. It is possible to use a definite number of statements from the book as exercises for students because their proofs are not given in the book but left for the reader.

An Advanced Complex Analysis Problem Book

Author : Daniel Alpay
ISBN : 9783319160597
Genre : Mathematics
File Size : 59. 37 MB
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This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.

Infinite Matrices And The Gliding Hump

Author : Charles Swartz
ISBN : 9789810227364
Genre : Mathematics
File Size : 27. 59 MB
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These notes present a theorem on infinite matrices with values in a topological group due to P Antosik and J Mikusinski. Using the matrix theorem and classical gliding hump techniques, a number of applications to various topics in functional analysis, measure theory and sequence spaces are given. There are a number of generalizations of the classical Uniform Boundedness Principle given; in particular, using stronger notions of sequential convergence and boundedness due to Antosik and Mikusinski, versions of the Uniform Boundedness Principle and the Banach-Steinhaus Theorem are given which, in contrast to the usual versions, require no completeness or barrelledness assumptions on the domain space. Versions of Nikodym Boundedness and Convergence Theorems of measure theory, the Orlicz-Pettis Theorem on subseries convergence, generalizations of the Schur Lemma on the equivalence of weak and norm convergence in l1 and the Mazur-Orlicz Theorem on the continuity of separately continuous bilinear mappings are also given. Finally, the matrix theorems are also employed to treat a number of topics in sequence spaces.

Infinite Matrices And The Gliding Hump

Author : C Swartz
ISBN : 9789814498715
Genre : Mathematics
File Size : 65. 89 MB
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These notes present a theorem on infinite matrices with values in a topological group due to P Antosik and J Mikusinski. Using the matrix theorem and classical gliding hump techniques, a number of applications to various topics in functional analysis, measure theory and sequence spaces are given. There are a number of generalizations of the classical Uniform Boundedness Principle given; in particular, using stronger notions of sequential convergence and boundedness due to Antosik and Mikusinski, versions of the Uniform Boundedness Principle and the Banach-Steinhaus Theorem are given which, in contrast to the usual versions, require no completeness or barrelledness assumptions on the domain space. Versions of Nikodym Boundedness and Convergence Theorems of measure theory, the Orlicz-Pettis Theorem on subseries convergence, generalizations of the Schur Lemma on the equivalence of weak and norm convergence in l1 and the Mazur-Orlicz Theorem on the continuity of separately continuous bilinear mappings are also given. Finally, the matrix theorems are also employed to treat a number of topics in sequence spaces. Contents:IntroductionThe Antosik-Mikusinski Matrix Theoremk-Convergence and k-BoundednessThe Uniform Boundedness PrincipleThe Banach-Steinhaus TheoremContinuity and Hypocontinuity for Bilinear MapsPap's Adjoint TheoremVector Versions of the Hahn-Schur TheoremsAn Abstract Hahn-Schur TheoremThe Orlicz-Pettis TheoremImbedding c0 and l∞Sequence Spaces Readership: Graduate students in pure mathematics. keywords:Gliding Hump;Uniform Boundedness;Antosik-Mikusinski Matrix Theorem;Bilinear Operators;Hahn-Schur Theorems;Orlicz-Pettis Theorems;Sequence Spaces;Adjoint Operators;Automatic Continuity;Banach-Steinhaus Theorems “… the book is very well written and can be used by doctoral students that have followed a usual course on functional analysis and are starting to work in any of the topics covered by the book, and researchers interested in barrelled spaces and sequence spaces.” Mathematical Reviews

Abstract Duality Pairs In Analysis

Author : Swartz Charles W
ISBN : 9789813232785
Genre : Mathematics
File Size : 72. 29 MB
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The book presents a theory of abstract duality pairs which arises by replacing the scalar field by an Abelian topological group in the theory of dual pair of vector spaces. Examples of abstract duality pairs are vector valued series, spaces of vector valued measures, spaces of vector valued integrable functions, spaces of linear operators and vector valued sequence spaces. These examples give rise to numerous applications such as abstract versions of the Orlicz–Pettis Theorem on subseries convergent series, the Uniform Boundedness Principle, the Banach–Steinhaus Theorem, the Nikodym Convergence theorems and the Vitali–Hahn–Saks Theorem from measure theory and the Hahn–Schur Theorem from summability. There are no books on the current market which cover the material in this book. Readers will find interesting functional analysis and the many applications to various topics in real analysis. Contents: Preface Abstract Duality Pairs or Abstract Triples Subseries Convergence Bounded Multiplier Convergent Series Multiplier Convergent Series The Uniform Boundedness Principle Banach–Steinhaus Biadditive and Bilinear Operators Triples with Projections Weak Compactness in Triples Appendices: Topology Sequence Spaces Boundedness Criterion Drewnowski Antosik–Mikusinski Matrix Theorems References Index Readership: Graduate Students and researchers in functional analysis. Keywords: Duality;Convergent Series;Orlicz-Pettis;Integrals;Measures;Sequence Spaces;Uniform BoundednessReview: Key Features: The book should be of interest to people with interests in functional analysis Readers should find interesting the many applications to various topics in real analysis There are no books on the current market which cover the material in the book

Acta Scientiarum Mathematicarum

Author :
ISBN : UCAL:B3689418
Genre : Mathematics
File Size : 47. 25 MB
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Topological Vector Spaces And Their Applications

Author : Vladimir I. Bogachev
ISBN : 9783319571171
Genre : Mathematics
File Size : 58. 7 MB
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This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. Overall, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.

Journal Of Natural Sciences And Mathematics

Author :
ISBN : UOM:39015056608089
Genre : Science
File Size : 88. 27 MB
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Studia Scientiarum Mathematicarum Hungarica

Author :
ISBN : UOM:39015046571470
Genre : Mathematics
File Size : 36. 88 MB
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