Fredholm and Local Spectral Theory, with Applications to Multipliers by Pietro AienaFredholm and Local Spectral Theory, with Applications to Multipliers by Pietro Aiena

Fredholm and Local Spectral Theory, with Applications to Multipliers

byPietro Aiena

Paperback | December 1, 2010

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This book shows the deep interaction between two important theories: Fredholm and local spectral theory. A particular emphasis is placed on the applications to multipliers and in particular to convolution operators. The book also presents some important progress, made in recent years, in the study of perturbation theory for classes of operators which occur in Fredholm theory.
Title:Fredholm and Local Spectral Theory, with Applications to MultipliersFormat:PaperbackDimensions:458 pages, 9.25 × 6.1 × 0.07 inPublished:December 1, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048165229

ISBN - 13:9789048165223

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Table of Contents

Preface1. The Kato decomposition property1. Hyper-kernel and hyper-range of an operator2. Semi-regular operators on Banach spaces3. Analytical core of an operator4. The semi-regular spectrum of an operator5. The generalized Kato decomposition6. Semi-Fredholm operators7. Quasi-nilpotent part of an operator2. The single-valued extension property1. Local spectrum and SVEP2. The SVEP at a point3. A local spectral mapping theorem4. Algebraic spectral subspaces5. Weighted shift operators and SVEP3. The SVEP and Fredholm theory1. Ascent, descent, and the SVEP2. The SVEP for operators of Kato type3. The SVEP on the components of rho kappa (T)4. The Fredholm, Weyl, and Browder spectra5. Compressions6. Some spectral mapping theorems7. Isolated points of the spectrum8. Weyl's theorem9. Riesz operators10. The spectra of some operators4. Multipliers of commutative Banach algebras1. Definitions and elementary properties2. The Helgason-Wang function3. The first spectral properties of multipliers4. Multipliers of group algebras5. Multipliers of Banach algebras with orthogonal basis6. Multipliers of commutative H* algebras5. Abstract Fredholm theory1. Inessential ideals2. The socle3. The socle of semi-prime Banach algebras4. Riesz algebras5. Fredholm elements of Banach algebras6. Compact multipliers7. Weyl multipliers8. Multipliers of Tauberian regular commutative algebras9. Some concrete cases10. Browder spectrum of a multiplier6. Decomposability1. Spectral maximal subspaces2. Decomposable operators on Banach spaces3. Super-decomposable operators4. Decomposable right shift operators5. Decomposable multipliers6. Riesz multipliers7. Decomposable convolution operators7. Perturbation classes of operators1. Inessential operators between Banach spaces2. Omega+ and Omega- operators3. Strictly singular and strictly cosingular operators4. Improjective operators5. Incomparability between Banach spacesBibliographyIndex

Editorial 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)