Introduction to Local Spectral Theory

Hardcover | April 6, 2000

byKjeld Laursen, Michael Neumann

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Modern local spectral theory is built on the classical spectral theorem, a fundamental result in single-operator theory and Hilbert spaces. This book provides an in-depth introduction to the natural expansion of this fascinating topic of Banach space operator theory, whose pioneers includeDunford, Bishop, Foias, and others. Assuming only modest prerequisites of its readership, it gives complete coverage of the field, including the fundamental recent work by Albrecht and Eschmeier which provides the full duality theory for Banach space operators. It is highlighted by manycharacterizations of decomposable operators, and of other related, important classes of operators, as well as an in-depth study of their spectral properties, including identifications of distinguished parts, and results on permanence properties of spectra with respect to several types of similarity.Also found is a thorough and quite elementary treatment of the modern single- operator duality theory; this theory has many applications, both to general issues of classification and to such celebrated problems as the invariant subspace problems. A long chapter - almost a book in itself - is devotedto the use of local spectral theory in the study of spectral properties of multipliers and convolution operators. Another one describes its connections to automatic continuity theory. Written in a careful and detailed style, it contains numerous examples, many simplified proofs of classical results,and extensive references. It concludes with a list of interesting open problems, suitable for continued research.

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From the Publisher

Modern local spectral theory is built on the classical spectral theorem, a fundamental result in single-operator theory and Hilbert spaces. This book provides an in-depth introduction to the natural expansion of this fascinating topic of Banach space operator theory, whose pioneers includeDunford, Bishop, Foias, and others. Assuming on...

Kjeld Bagger Laursen Department of Mathematics University of Copenhagen Universitetsparken 5 DK-2100 COPENHAGEN, DENMARK Tel. +45 35320690 Fax: +45 35320704 Email: laursen@math.ku.dk Michael M Neumann Department of Mathematics and Statistics Mississippi State University P.O. Drawer MA Mississippi State, MS 39762 USA Tel.: +1 662 ...
Format:HardcoverPublished:April 6, 2000Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198523815

ISBN - 13:9780198523819

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Table of Contents

1. Decomposable operators2. Functional models, duality theory, and invariant subspaces3. The spectrum and spectral inclusions4. Local spectral theory for multipliers5. Connections to automatic continuity6. Open problemsAppendixBibliographyIndex of notationIndex

Editorial Reviews

'...gives a rigorous development of local soectral theory to bounded linear operators on Banach spaces, with the major emphasis being on single operators' Aslib