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Mathematics - Analysis | Biorthogonal Systems in Banach Spaces

Biorthogonal Systems in Banach Spaces

Hajek, P., Montesinos Santalucia, V., Vanderwerff, J., Zizler, V.

2008, XVIII, 339 p.

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  • Offers notes and exercises related to the topic
  • Presents open problems and possible directions of research in each chapter
  • Reviews current avenues of research in biorthogonal systems in Banach spaces

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.

Content Level » Research

Keywords » Banach Space - banach spaces - functional analysis

Related subjects » Analysis - Security and Cryptology

Table of contents 

Separable Banach Spaces.- Universality and the Szlenk Index.- Review of Weak Topology and Renormings.- Biorthogonal Systems in Nonseparable Spaces.- Markushevich Bases.- Weak Compact Generating.- Transfinite Sequence Spaces.- More Applications.

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