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Fredholm and Local Spectral Theory, with Applications to Multipliers

  • Book
  • © 2004

Overview

Authors:
  1. Pietro Aiena

    1. Dipartimento di Matematica ed Applicazioni, Università di Palermo, Palermo, Italy

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiv
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  2. The Kato decomposition property

    Pages 1-53

  3. The single-valued extension property

    Pages 55-107

  4. The SVEP and Fredholm theory

    Pages 109-190

  5. Multipliers of commutative Banach algebras

    Pages 191-237

  6. Abstract Fredholm theory

    Pages 239-308

  7. Decomposability

    Pages 309-366

  8. Perturbation classes of operators

    Pages 367-421

  9. Back Matter

    Pages 423-444
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Keywords

About this book

A signi?cant sector of the development of spectral theory outside the classical area of Hilbert space may be found amongst at multipliers de?ned on a complex commutative Banach algebra A. Although the general theory of multipliers for abstract Banach algebras has been widely investigated by several authors, it is surprising how rarely various aspects of the spectral theory, for instance Fredholm theory and Riesz theory, of these important classes of operators have been studied. This scarce consideration is even more surprising when one observes that the various aspects of spectral t- ory mentioned above are quite similar to those of a normal operator de?ned on a complex Hilbert space. In the last ten years the knowledge of the spectral properties of multip- ers of Banach algebras has increased considerably, thanks to the researches undertaken by many people working in local spectral theory and Fredholm theory. This research activity recently culminated with the publication of the book of Laursen and Neumann [214], which collects almost every thing that is known about the spectral theory of multipliers.

Reviews

From the reviews of the first edition:

"The primary goal of this monograph is a presentation of the Fredholm and Riesz theory of Banach space operators and applications in the stetting of multipliers of a commutative Banach algebra. … This book complements standard references for Fredholm theory … on the one hand, and Laursen and Neumann’s book on the other hand. It should prove to be a valuable resource for graduate students and researchers in Banach space operator theory." (Thomas Len Miller, Mathematical Reviews, 2005e)

"The main concern of the monograph under review is Fredholm theory and its connections with the local spectral theory for bounded linear operators in Banach spaces. … The monograph is intended for the use of researchers and graduate students in functional analysis, having a certain background in operator theory. The style is alert and pleasant and there is a fair and state-of-the-art account of the actual Fredholm theory in connection with local spectral theory." (Florian-Horia Vasilescu, Zentralblatt MATH,Vol. 1077 (3), 2006)

Authors and Affiliations

  • Dipartimento di Matematica ed Applicazioni, Università di Palermo, Palermo, Italy

    Pietro Aiena

Bibliographic Information

  • Book Title: Fredholm and Local Spectral Theory, with Applications to Multipliers

  • Authors: Pietro Aiena

  • DOI: https://doi.org/10.1007/1-4020-2525-4

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2004

  • Hardcover ISBN: 978-1-4020-1830-5Published: 29 February 2004

  • Softcover ISBN: 978-90-481-6522-3Published: 01 December 2010

  • eBook ISBN: 978-1-4020-2525-9Published: 08 May 2007

  • Edition Number: 1

  • Number of Pages: XIV, 444

  • Topics: Operator Theory, Functional Analysis, Abstract Harmonic Analysis

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