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This title in other editions

Other titles in the CMS Books in Mathematics series:

Biorthogonal Systems in Banach Spaces (CMS Books in Mathematics)

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Biorthogonal Systems in Banach Spaces (CMS Books in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

The main theme of this book is the relation between the global structure of Banach spaces and the various types of generalized "coordinate systems" - or "bases" - they possess.  This subject is not new and has been investigated since the inception of the study of Banach spaces.  In this book, the authors systematically investigate the concepts of Markushevich bases, fundamental systems, total systems and their variants. The material naturally splits into the case of separable Banach spaces, as is treated in the first two chapters, and the nonseparable case, which is covered in the remainder of the book.  This book contains new results, and a substantial portion of this material has never before appeared in book form.  The book will be of interest to both researchers and graduate students. Topics covered in this book include: - Biorthogonal Systems in Separable Banach Spaces - Universality and Szlenk Index - Weak Topologies and Renormings - Biorthogonal Systems in Nonseparable Spaces - Transfinite Sequence Spaces - Applications Petr Hájek is Professor of Mathematics at the Mathematical Institute of the Academy of Sciences of the Czech Republic.  Vicente Montesinos is Professor of Mathematics at the Polytechnic University of Valencia, Spain.  Jon Vanderwerff is Professor of Mathematics at La Sierra University, in Riverside, California.  Václav Zizler is Professor of Mathematics at the Mathematical Institute of the Academy of Sciences of the Czech Republic.

Synopsis:

This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces. It achieves this in a manner accessible to graduate students and researchers who have a foundation in Banach space theory. The authors have included numerous exercises, as well as open problems that point to possible directions of research.

Synopsis:

One of the fundamental questions of Banach space theory is whether every Banach space has a basis. A space with a basis gives us the feeling of familiarity and concreteness, and perhaps a chance to attempt the classification of all Banach spaces and other problems. The main goals of this book are to: • introduce the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces; • to do so in a manner accessible to graduate students and researchers who have a foundation in Banach space theory; • expose the reader to some current avenues of research in biorthogonal systems in Banach spaces; • provide notes and exercises related to the topic, as well as suggesting open problems and possible directions of research. The intended audience will have a basic background in functional analysis. The authors have included numerous exercises, as well as open problems that point to possible directions of research.

Table of Contents

Biorthogonal Systems in Separable Spaces.- Universality and Szlenk Index.- Biorthogonal systems in nonseparable spaces.- Weakly Lindelof detemined spaces.- Weakly compactly generated spaces.- Geometry of spaces with fundamental biorthogonal systems.

Product Details

ISBN:
9780387689142
Author:
Hajek, Petr
Publisher:
Springer
Author:
Montesinos Santalucia, Vicente
Author:
Zizler, Vaclav
Author:
Vanderwerff, Jon
Author:
Vicente Montesinos Santalucia
Subject:
Functional Analysis
Subject:
Banach spaces
Subject:
Biorthogonal systems.
Subject:
Mathematics : Functional Analysis
Subject:
Systems and Data Security
Copyright:
Edition Description:
Book
Series:
CMS Books in Mathematics
Publication Date:
20071115
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
360
Dimensions:
235 x 155 mm

Related Subjects

Science and Mathematics » Mathematics » Algebra » Other
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Topology

Biorthogonal Systems in Banach Spaces (CMS Books in Mathematics) New Hardcover
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Product details 360 pages Springer - English 9780387689142 Reviews:
"Synopsis" by , This book introduces the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces. It achieves this in a manner accessible to graduate students and researchers who have a foundation in Banach space theory. The authors have included numerous exercises, as well as open problems that point to possible directions of research.
"Synopsis" by , One of the fundamental questions of Banach space theory is whether every Banach space has a basis. A space with a basis gives us the feeling of familiarity and concreteness, and perhaps a chance to attempt the classification of all Banach spaces and other problems. The main goals of this book are to: • introduce the reader to some of the basic concepts, results and applications of biorthogonal systems in infinite dimensional geometry of Banach spaces, and in topology and nonlinear analysis in Banach spaces; • to do so in a manner accessible to graduate students and researchers who have a foundation in Banach space theory; • expose the reader to some current avenues of research in biorthogonal systems in Banach spaces; • provide notes and exercises related to the topic, as well as suggesting open problems and possible directions of research. The intended audience will have a basic background in functional analysis. The authors have included numerous exercises, as well as open problems that point to possible directions of research.
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