Descriptive Topology in Selected Topics of Functional Analysis

Descriptive Topology in Selected Topics of Functional Analysis

Author: Jerzy Kąkol

Publisher: Springer Science & Business Media

Published: 2011-08-30

Total Pages: 494

ISBN-13: 1461405297

DOWNLOAD EBOOK

"Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Fréchet spaces, (LF)-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in functional analysis in distribution theory, differential equations, complex analysis, and various other analytical settings. This monograph provides new insights into the connections between the topological properties of linear function spaces and their applications in functional analysis.


Descriptive Topology and Functional Analysis II

Descriptive Topology and Functional Analysis II

Author: Juan Carlos Ferrando

Publisher: Springer

Published: 2019-06-02

Total Pages: 302

ISBN-13: 3030173763

DOWNLOAD EBOOK

This book is the result of a meeting on Topology and Functional Analysis, and is dedicated to Professor Manuel López-Pellicer's mathematical research. Covering topics in descriptive topology and functional analysis, including topological groups and Banach space theory, fuzzy topology, differentiability and renorming, tensor products of Banach spaces and aspects of Cp-theory, this volume is particularly useful to young researchers wanting to learn about the latest developments in these areas.


Descriptive Topology and Functional Analysis

Descriptive Topology and Functional Analysis

Author: Juan Carlos Ferrando

Publisher: Springer

Published: 2016-09-17

Total Pages: 0

ISBN-13: 9783319381510

DOWNLOAD EBOOK

Descriptive topology and functional analysis, with extensive material demonstrating new connections between them, are the subject of the first section of this work. Applications to spaces of continuous functions, topological Abelian groups, linear topological equivalence and to the separable quotient problem are included and are presented as open problems. The second section is devoted to Banach spaces, Banach algebras and operator theory. Each chapter presents a lot of worthwhile and important recent theorems with an abstract discussing the material in the chapter. Each chapter can almost be seen as a survey covering a particular area.


Functional Analysis and Continuous Optimization

Functional Analysis and Continuous Optimization

Author: José M. Amigó

Publisher: Springer Nature

Published: 2023-07-01

Total Pages: 273

ISBN-13: 3031300149

DOWNLOAD EBOOK

The book includes selected contributions presented at the "International Meeting on Functional Analysis and Continuous Optimization" held in Elche (Spain) on June 16–17, 2022. Its contents cover very recent results in functional analysis, continuous optimization and the interplay between these disciplines. Therefore, this book showcases current research on functional analysis and optimization with individual contributions, as well as new developments in both areas. As a result, the reader will find useful information and stimulating ideas.


Topological Vector Spaces and Their Applications

Topological Vector Spaces and Their Applications

Author: V.I. Bogachev

Publisher: Springer

Published: 2017-05-16

Total Pages: 466

ISBN-13: 3319571176

DOWNLOAD EBOOK

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.


Advanced Courses Of Mathematical Analysis V - Proceedings Of The Fifth International School

Advanced Courses Of Mathematical Analysis V - Proceedings Of The Fifth International School

Author: Juan Carlos Navarro Pascual

Publisher: World Scientific

Published: 2016-06-24

Total Pages: 319

ISBN-13: 9814699705

DOWNLOAD EBOOK

This volume contains recent papers by several specialists in different fields of mathematical analysis. It offers a reasonably wide perspective of the current state of research, and new trends, in areas related to measure theory, harmonic analysis, non-associative structures in functional analysis and summability in locally convex spaces.Those interested in researching any areas of mathematical analysis will find here numerous suggestions on possible topics with an important impact today. Often, the contributions are presented in an expository nature and this makes the discussed topics accessible to a more general audience.


A Cp-Theory Problem Book

A Cp-Theory Problem Book

Author: Vladimir V. Tkachuk

Publisher: Springer

Published: 2016-04-05

Total Pages: 740

ISBN-13: 3319243853

DOWNLOAD EBOOK

This fourth volume in Vladimir Tkachuk's series on Cp-theory gives reasonably complete coverage of the theory of functional equivalencies through 500 carefully selected problems and exercises. By systematically introducing each of the major topics of Cp-theory, the book is intended to bring a dedicated reader from basic topological principles to the frontiers of modern research. The book presents complete and up-to-date information on the preservation of topological properties by homeomorphisms of function spaces. An exhaustive theory of t-equivalent, u-equivalent and l-equivalent spaces is developed from scratch. The reader will also find introductions to the theory of uniform spaces, the theory of locally convex spaces, as well as the theory of inverse systems and dimension theory. Moreover, the inclusion of Kolmogorov's solution of Hilbert's Problem 13 is included as it is needed for the presentation of the theory of l-equivalent spaces. This volume contains the most important classical results on functional equivalencies, in particular, Gul'ko and Khmyleva's example of non-preservation of compactness by t-equivalence, Okunev's method of constructing l-equivalent spaces and the theorem of Marciszewski and Pelant on u-invariance of absolute Borel sets.


Banach Space Theory

Banach Space Theory

Author: Marián Fabian

Publisher: Springer Science & Business Media

Published: 2011-02-04

Total Pages: 820

ISBN-13: 1441975152

DOWNLOAD EBOOK

Banach spaces provide a framework for linear and nonlinear functional analysis, operator theory, abstract analysis, probability, optimization and other branches of mathematics. This book introduces the reader to linear functional analysis and to related parts of infinite-dimensional Banach space theory. Key Features: - Develops classical theory, including weak topologies, locally convex space, Schauder bases and compact operator theory - Covers Radon-Nikodým property, finite-dimensional spaces and local theory on tensor products - Contains sections on uniform homeomorphisms and non-linear theory, Rosenthal's L1 theorem, fixed points, and more - Includes information about further topics and directions of research and some open problems at the end of each chapter - Provides numerous exercises for practice The text is suitable for graduate courses or for independent study. Prerequisites include basic courses in calculus and linear. Researchers in functional analysis will also benefit for this book as it can serve as a reference book.