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Spectral Theory of Linear Operators

and Spectral Systems in Banach Algebras

  • Vladimir Müller

Part of the Operator Theory: Advances and Applications book series (OT, volume 139)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Pages 1-83
  3. Pages 85-147
  4. Pages 149-236
  5. Pages 237-310
  6. Pages 311-391
  7. Back Matter
    Pages 393-439

About this book

Introduction

This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants.

The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed.

The monograph should appeal both to students who would like to learn about spectral theory and to experts in the field. It can also serve as a reference book.

The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem.

 

This book is dedicated to the spectral theory of linear operators on Banach spaces and of elements in Banach algebras. It presents a survey of results concerning various types of spectra, both of single and n-tuples of elements. Typical examples are the one-sided spectra, the approximate point, essential, local and Taylor spectrum, and their variants.

The theory is presented in a unified, axiomatic and elementary way. Many results appear here for the first time in a monograph. The material is self-contained. Only a basic knowledge of functional analysis, topology, and complex analysis is assumed.

The present second edition contains a number of new results, in particular, concerning orbits and their relations to the invariant subspace problem.

 

Due to its very clear style and the careful organization of the material, this truly brilliant book may serve as an introduction into the field, yet it also provides an excellent source of information on specific topics in spectral theory for the working mathematician.

Review of the first edition by M. Grosser, Vienna

Monatshefte für Mathematik Vol. 146, No. 1/2005

Keywords

Banach algebra algebra banach spaces complex analysis field functional analysis integral integral equation matrix operator operator theory spectral theory

Authors and affiliations

  • Vladimir Müller
    • 1
  1. 1.Institute of MathematicsCzech Academy of SciencesPraha 1Czech Republic

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-7643-8265-0
  • Copyright Information Birkhäuser Verlag AG, P.O. Box 133, CH-4010 Basel, Switzerland 2007
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-7643-8264-3
  • Online ISBN 978-3-7643-8265-0
  • Buy this book on publisher's site