Fredholm and Local Spectral Theory, with Applications to Multipliers

Authors: Aiena, Pietro

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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)


Table of contents (7 chapters)

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-1-4020-2525-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-1-4020-1830-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-90-481-6522-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Fredholm and Local Spectral Theory, with Applications to Multipliers
Authors
Copyright
2004
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-1-4020-2525-9
DOI
10.1007/1-4020-2525-4
Hardcover ISBN
978-1-4020-1830-5
Softcover ISBN
978-90-481-6522-3
Edition Number
1
Number of Pages
XIV, 444
Topics