Semitopological Vector Spaces

Hypernorms, Hyperseminorms, and Operators

Author: Mark Burgin

Publisher: CRC Press

ISBN: 1771885351

Category: Mathematics

Page: 476

View: 5773

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.
Posted in Mathematics

Abstract Duality Pairs In Analysis

Author: Swartz Charles W

Publisher: World Scientific

ISBN: 9813232781

Category: Mathematics

Page: 304

View: 9903

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: PrefaceAbstract Duality Pairs or Abstract TriplesSubseries ConvergenceBounded Multiplier Convergent SeriesMultiplier Convergent SeriesThe Uniform Boundedness PrincipleBanach–SteinhausBiadditive and Bilinear OperatorsTriples with ProjectionsWeak Compactness in TriplesAppendices: TopologySequence SpacesBoundedness CriterionDrewnowskiAntosik–Mikusinski Matrix TheoremsReferencesIndex 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 analysisReaders should find interesting the many applications to various topics in real analysisThere are no books on the current market which cover the material in the book
Posted in Mathematics

Topological Vector Spaces and Their Applications

Author: Vladimir I. Bogachev,Oleg Smolyanov

Publisher: Springer

ISBN: 3319571176

Category: Mathematics

Page: 456

View: 834

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.
Posted in Mathematics

The American Mathematical Monthly

The Official Journal of the Mathematical Association of America

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematicians

Page: N.A

View: 2942

Posted in Mathematicians

Topological Vector Spaces, Algebras and Related Areas

Author: A Lau,I Tweddle

Publisher: CRC Press

ISBN: 9780582257771

Category: Mathematics

Page: 280

View: 2373

This volume contains the proceedings of an international conference held to mark the retirement of Professor Taqdir Husain from McMaster University. The contributions, covering topics such as topological vector spaces, topological algebras and related areas, reflect Husain's research interests and present surveys and new research in the topics of the conference.
Posted in Mathematics

Reviews in Functional Analysis, 1980-86

As Printed in Mathematical Reviews

Author: N.A

Publisher: Amer Mathematical Society

ISBN: N.A

Category: Mathematics

Page: 2461

View: 3506

These four volumes contain the almost 12,000 reviews appearing in Mathematical Reviews under primary or secondary subject classification 46, Functional Analysis, between 1980 and 1986.
Posted in Mathematics

Algebraic Topology of Finite Topological Spaces and Applications

Author: Jonathan A. Barmak

Publisher: Springer Science & Business Media

ISBN: 3642220029

Category: Mathematics

Page: 170

View: 866

This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen's conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.
Posted in Mathematics

Topology for Analysis

Author: Albert Wilansky

Publisher: Courier Corporation

ISBN: 0486469034

Category: Mathematics

Page: 383

View: 7135

Starting with the first principles of topology, this volume advances to general analysis. Three levels of examples and problems make it appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important concepts, and a 40-page appendix includes tables of theorems and counterexamples. 1970 edition.
Posted in Mathematics

Counterexamples in Topology

Author: Lynn Arthur Steen,J. Arthur Seebach

Publisher: Courier Corporation

ISBN: 0486319296

Category: Mathematics

Page: 272

View: 2325

Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Numerous problems and exercises correlated with examples. 1978 edition. Bibliography.
Posted in Mathematics

Lecture notes in mathematics

Author: Albrecht Dold

Publisher: N.A

ISBN: N.A

Category: Differentiable functions

Page: N.A

View: 680

Posted in Differentiable functions

Topological Vector Spaces and Distributions

Author: John Horvath

Publisher: Courier Corporation

ISBN: 0486311031

Category: Mathematics

Page: 464

View: 5493

"The most readable introduction to the theory of vector spaces available in English and possibly any other language."—J. L. B. Cooper, MathSciNet Review Mathematically rigorous but user-friendly, this classic treatise discusses major modern contributions to the field of topological vector spaces. The self-contained treatment includes complete proofs for all necessary results from algebra and topology. Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers. The precise exposition of the first three chapters—covering Banach spaces, locally convex spaces, and duality—provides an excellent summary of the modern theory of locally convex spaces. The fourth and final chapter develops the theory of distributions in relation to convolutions, tensor products, and Fourier transforms. Augmented with many examples and exercises, the text includes an extensive bibliography.
Posted in Mathematics

Topological Vector Spaces

Author: H.H. Schaefer

Publisher: Springer Science & Business Media

ISBN: 1468499289

Category: Mathematics

Page: 296

View: 3837

The present book is intended to be a systematic text on topological vector spaces and presupposes familiarity with the elements of general topology and linear algebra. The author has found it unnecessary to rederive these results, since they are equally basic for many other areas of mathematics, and every beginning graduate student is likely to have made their acquaintance. Simi larly, the elementary facts on Hilbert and Banach spaces are widely known and are not discussed in detail in this book, which is mainly addressed to those readers who have attained and wish to get beyond the introductory level. The book has its origin in courses given by the author at Washington State University, the University of Michigan, and the University of Tiibingen in the years 1958-1963. At that time there existed no reasonably complete text on topological vector spaces in English, and there seemed to be a genuine need for a book on this subject. This situation changed in 1963 with the appearance of the book by Kelley, Namioka et al. [1] which, through its many elegant proofs, has had some influence on the final draft of this manuscript. Yet the two books appear to be sufficiently different in spirit and subject matter to justify the publication of this manuscript; in particular, the present book includes a discussion of topological tensor products, nuclear spaces, ordered topological vector spaces, and an appendix on positive operators.
Posted in Mathematics

Essential Topology

Author: Martin D. Crossley

Publisher: Springer Science & Business Media

ISBN: 9781852337827

Category: Mathematics

Page: 224

View: 698

This thoroughly modern introduction to undergraduate topology brings the most exciting and useful aspects of modern topology to the reader. Containing all the key results of basic topology, this book concentrates on uniting the most interesting aspects of the subject with aspects that are most useful to research. It is suitable for self-study, and will leave the reader both motivated and well prepared for further study.
Posted in Mathematics