A Short Course on Banach Space Theory PDF Download

Author: N. L. Carothers
Publisher: Cambridge University Press
ISBN: 0521842832
Category : Mathematics
Languages : en
Pages : 199

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Author: Fernando Albiac
Publisher: Springer
ISBN: 3319315579
Category : Mathematics
Languages : en
Pages : 508

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Book Description
This text provides the reader with the necessary technical tools and background to reach the frontiers of research without the introduction of too many extraneous concepts. Detailed and accessible proofs are included, as are a variety of exercises and problems. The two new chapters in this second edition are devoted to two topics of much current interest amongst functional analysts: Greedy approximation with respect to bases in Banach spaces and nonlinear geometry of Banach spaces. This new material is intended to present these two directions of research for their intrinsic importance within Banach space theory, and to motivate graduate students interested in learning more about them. This textbook assumes only a basic knowledge of functional analysis, giving the reader a self-contained overview of the ideas and techniques in the development of modern Banach space theory. Special emphasis is placed on the study of the classical Lebesgue spaces Lp (and their sequence space analogues) and spaces of continuous functions. The authors also stress the use of bases and basic sequences techniques as a tool for understanding the isomorphic structure of Banach spaces. From the reviews of the First Edition: "The authors of the book...succeeded admirably in creating a very helpful text, which contains essential topics with optimal proofs, while being reader friendly... It is also written in a lively manner, and its involved mathematical proofs are elucidated and illustrated by motivations, explanations and occasional historical comments... I strongly recommend to every graduate student who wants to get acquainted with this exciting part of functional analysis the instructive and pleasant reading of this book..."—Gilles Godefroy, Mathematical Reviews

Author: Robert E. Megginson
Publisher: Springer Science & Business Media
ISBN: 9780387984315
Category : Mathematics
Languages : en
Pages : 636

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Book Description
This book is an introduction to the general theory of Banach spaces, designed to prepare the reader with a background in functional analysis that will enable him or her to tackle more advanced literature in the subject. The book is replete with examples, historical notes, and citations, as well as nearly 500 exercises.

Author: Bor-Luh Lin
Publisher: American Mathematical Soc.
ISBN: 082185092X
Category : Mathematics
Languages : en
Pages : 521

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Book Description
This volume contains the proceedings from a Research Workshop on Banach Space Theory held at the University of Iowa in Iowa City in July 1987. The workshop provided participants with a collaborative working atmosphere in which ideas could be exchanged informally. Several papers were initiated during the workshop and are presented here in their final form. Also included are contributions from several experts who were unable to attend the workshop. None of the papers will be published elsewhere. During the workshop, two hours each day were devoted to seminars on current problems in such areas as weak Hilbert spaces, zonoids, analytic martingales, and operator theory, and these topics are reflected in some of the papers in the collection.

Author: Klaus-Jochen Engel
Publisher: Springer Science & Business Media
ISBN: 0387313419
Category : Mathematics
Languages : en
Pages : 257

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Book Description
The book offers a direct and up-to-date introduction to the theory of one-parameter semigroups of linear operators on Banach spaces. The book is intended for students and researchers who want to become acquainted with the concept of semigroups.

Author: William Arveson
Publisher: Springer Science & Business Media
ISBN: 0387953000
Category : Mathematics
Languages : en
Pages : 140

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Book Description
This book presents the basic tools of modern analysis within the context of the fundamental problem of operator theory: to calculate spectra of specific operators on infinite dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra: the mathematical foundations of quantum physics, noncommutative K-theory, and the classification of simple C*-algebras being three areas of current research activity which require mastery of the material presented here.

Author: Robert E. Megginson
Publisher: Springer Science & Business Media
ISBN: 1461206030
Category : Mathematics
Languages : en
Pages : 613

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Book Description
Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.

Author: William Arveson
Publisher: Springer Science & Business Media
ISBN: 0387215182
Category : Mathematics
Languages : en
Pages : 143

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Book Description
This book presents the basic tools of modern analysis within the context of the fundamental problem of operator theory: to calculate spectra of specific operators on infinite dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra: the mathematical foundations of quantum physics, noncommutative K-theory, and the classification of simple C*-algebras being three areas of current research activity which require mastery of the material presented here.

Author: Marián Fabian
Publisher: Springer Science & Business Media
ISBN: 1441975152
Category : Mathematics
Languages : en
Pages : 820

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Book Description
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.

Author: P. Wojtaszczyk
Publisher: Cambridge University Press
ISBN: 9780521566759
Category : Mathematics
Languages : en
Pages : 400

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Book Description
This book is intended to be used with graduate courses in Banach space theory.