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Semigroups of operators and an application to spectral theory

Published online by Cambridge University Press:  24 October 2008

W. Ricker
W. Ricker
Affiliation:
University of Adelaide, Australia
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Extract

A problem of fundamental importance in Spectral Theory consists of finding criteria for an operator to be of scalar-type in the sense of N. Dunford [1]. One relatively general approach in determining such criteria is based on the method of integral transforms (see for example [4], [5], [6], [11], [12]). For example, if X is a Banach space and T is a continuous linear operator on X, then the group {eitT; t real} exists. As noted by several authors (e.g. [4], [6]), this group can then be effectively used for analysing the operator T.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 96 , Issue 1 , July 1984 , pp. 143 - 149
Copyright
Copyright © Cambridge Philosophical Society 1984

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