Biorthogonal Systems in Banach Spaces

  • Petr Hájek
  • Vicente Montesinos Santalucía
  • Jon Vanderwerff
  • Václav Zizler

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Pages 165-206
  3. Pages 207-240
  4. Pages 273-302
  5. Back Matter
    Pages 303-339

About this book

Introduction

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.

Keywords

Banach Space banach spaces functional analysis

Authors and affiliations

  • Petr Hájek
    • 1
  • Vicente Montesinos Santalucía
    • 2
  • Jon Vanderwerff
    • 3
  • Václav Zizler
    • 1
  1. 1.Mathematical Institute of the Czech Academy of Sciences11567The Czech Republic
  2. 2.Universidad Politécnica de Valencia46022Spain
  3. 3.Mathematics and Computer Science DepartmentLa Sierra UniversityRiversideUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-68915-9
  • Copyright Information Springer Science+Business Media, LLC 2008
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-68914-2
  • Online ISBN 978-0-387-68915-9
  • About this book