An Introduction to Local Spectral Theory

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ID: 307083
2000
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Abstract
Abstract 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 include Dunford, 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 many characterizations 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 devoted to 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.
Reference Key
openalex_W1575570794 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Kjeld Laursen, Michael Neumann
Journal Oxford University Press eBooks
Year 2000
DOI
10.1093/oso/9780198523819.001.0001
URL
https://doi.org/10.1093/oso/9780198523819.001.0001
Keywords Keywords not found

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