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The Rademacher System in Function Spaces

2020-07-27 Mathematics
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Release : 2020-07-27
Genre : Mathematics
Kind : eBook
Book Rating : 904/5 ( reviews)

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Book Synopsis The Rademacher System in Function Spaces by : Sergey V. Astashkin

Download or read book The Rademacher System in Function Spaces written by Sergey V. Astashkin. This book was released on 2020-07-27. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic treatment of the Rademacher system, one of the most important unifying concepts in mathematics, and includes a number of recent important and beautiful results related to the Rademacher functions. The book discusses the relationship between the properties of the Rademacher system and geometry of some function spaces. It consists of three parts, in which this system is considered respectively in Lp-spaces, in general symmetric spaces and in certain classes of non-symmetric spaces (BMO, Paley, Cesaro, Morrey). The presentation is clear and transparent, providing all main results with detailed proofs. Moreover, literary and historical comments are given at the end of each chapter. This book will be suitable for graduate students and researchers interested in functional analysis, theory of functions and geometry of Banach spaces.

Schauder Bases in Banach Spaces of Continuous Functions

2006-11-14 Mathematics
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Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 436/5 ( reviews)

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Book Synopsis Schauder Bases in Banach Spaces of Continuous Functions by : Z. Semadeni

Download or read book Schauder Bases in Banach Spaces of Continuous Functions written by Z. Semadeni. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt:

Narrow Operators on Function Spaces and Vector Lattices

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 343/5 ( reviews)

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Book Synopsis Narrow Operators on Function Spaces and Vector Lattices by : Mikhail Popov

Download or read book Narrow Operators on Function Spaces and Vector Lattices written by Mikhail Popov. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Most classes of operators that are not isomorphic embeddings are characterized by some kind of a “smallness” condition. Narrow operators are those operators defined on function spaces that are “small” at {-1,0,1}-valued functions, e.g. compact operators are narrow. The original motivation to consider such operators came from theory of embeddings of Banach spaces, but since then they were also applied to the study of the Daugavet property and to other geometrical problems of functional analysis. The question of when a sum of two narrow operators is narrow, has led to deep developments of the theory of narrow operators, including an extension of the notion to vector lattices and investigations of connections to regular operators. Narrow operators were a subject of numerous investigations during the last 30 years. This monograph provides a comprehensive presentation putting them in context of modern theory. It gives an in depth systematic exposition of concepts related to and influenced by narrow operators, starting from basic results and building up to most recent developments. The authors include a complete bibliography and many attractive open problems.

Köthe-Bochner Function Spaces

2011-06-27 Mathematics
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Release : 2011-06-27
Genre : Mathematics
Kind : eBook
Book Rating : 884/5 ( reviews)

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Book Synopsis Köthe-Bochner Function Spaces by : Pei-Kee Lin

Download or read book Köthe-Bochner Function Spaces written by Pei-Kee Lin. This book was released on 2011-06-27. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the study of Köthe–Bochner function spaces, an active area of research at the intersection of Banach space theory, harmonic analysis, probability, and operator theory. A number of significant results---many scattered throughout the literature---are distilled and presented here, giving readers a comprehensive view of the subject from its origins in functional analysis to its connections to other disciplines. Considerable background material is provided, and the theory of Köthe–Bochner spaces is rigorously developed, with a particular focus on open problems. Extensive historical information, references, and questions for further study are included; instructive examples and many exercises are incorporated throughout. Both expansive and precise, this book’s unique approach and systematic organization will appeal to advanced graduate students and researchers in functional analysis, probability, operator theory, and related fields.

Lectures and Exercises on Functional Analysis

Mathematics
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Genre : Mathematics
Kind : eBook
Book Rating : 695/5 ( reviews)

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Book Synopsis Lectures and Exercises on Functional Analysis by : Александр Яковлевич Хелемский

Download or read book Lectures and Exercises on Functional Analysis written by Александр Яковлевич Хелемский. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt: The book is based on courses taught by the author at Moscow State University. Compared to many other books on the subject, it is unique in that the exposition is based on extensive use of the language and elementary constructions of category theory. Among topics featured in the book are the theory of Banach and Hilbert tensor products, the theory of distributions and weak topologies, and Borel operator calculus. The book contains many examples illustrating the general theory presented, as well as multiple exercises that help the reader to learn the subject. It can be used as a textbook on selected topics of functional analysis and operator theory. Prerequisites include linear algebra, elements of real analysis, and elements of the theory of metric spaces.

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