Operator Theory: Advances and Applications

Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras

Authors: Müller, Vladimir

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  • Unique collection of material in spectral theory that was only available in research papers before
  • Theory is presented in a unified, axiomatic and elementary way
  • Only a basic knowledge of functional analysis, topology, and complex analysis is assumed
  • Serves as a reference book on spectral theory in Banach algebras
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About this book

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

Table of contents (5 chapters)

Table of contents (5 chapters)

Buy this book

eBook $74.99
price for USA in USD
  • ISBN 978-3-0348-7788-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras
Authors
Series Title
Operator Theory: Advances and Applications
Series Volume
139
Copyright
2003
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-7788-6
DOI
10.1007/978-3-0348-7788-6
Series ISSN
0255-0156
Edition Number
1
Number of Pages
X, 382
Number of Illustrations
1 b/w illustrations
Topics