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Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras

  • Book
  • © 2003

Overview

Authors:
  1. Vladimir Müller

    1. Institute of Mathematics, Czech Academy of Sciences, Praha 1, Czech Republic

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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

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-x
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  2. Banach Algebras

    • Vladimir Müller
    Pages 1-79

  3. Operators

    • Vladimir Müller
    Pages 81-141

  4. Essential Spectrum

    • Vladimir Müller
    Pages 143-218

  5. Taylor Spectrum

    • Vladimir Müller
    Pages 219-286

  6. Orbits and Capacity

    • Vladimir Müller
    Pages 287-338

  7. Back Matter

    Pages 339-382
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Keywords

About this book

Spectral theory is an important part of functional analysis.It has numerous appli­ cations in many parts of mathematics and physics including matrix theory, func­ tion theory, complex analysis, differential and integral equations, control theory and quantum physics. In recent years, spectral theory has witnessed an explosive development. There are many types of spectra, both for one or several commuting operators, with important applications, for example the approximate point spectrum, Taylor spectrum, local spectrum, essential spectrum, etc. The present monograph is an attempt to organize the available material most of which exists only in the form of research papers scattered throughout the literature. The aim is to present a survey of results concerning various types of spectra in a unified, axiomatic way. The central unifying notion is that of a regularity, which in a Banach algebra is a subset of elements that are considered to be "nice". A regularity R in a Banach algebra A defines the corresponding spectrum aR(a) = {A E C : a - ,\ rJ. R} in the same way as the ordinary spectrum is defined by means of invertible elements, a(a) = {A E C : a - ,\ rJ. Inv(A)}. Axioms of a regularity are chosen in such a way that there are many natural interesting classes satisfying them. At the same time they are strong enough for non-trivial consequences, for example the spectral mapping theorem.

Authors and Affiliations

  • Institute of Mathematics, Czech Academy of Sciences, Praha 1, Czech Republic

    Vladimir Müller

Bibliographic Information

  • Book Title: Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras

  • Authors: Vladimir Müller

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-7788-6

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2003

  • eBook ISBN: 978-3-0348-7788-6Published: 11 November 2013

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: X, 382

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Operator Theory

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