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The spectral theorem for well-bounded operators

Part of: General theory of linear operators Special classes of linear operators Topological linear spaces and related structures Topological algebras, normed rings and algebras, Banach algebras

Published online by Cambridge University Press:  09 April 2009

Ian Doust  and
Qiu Bozhou
Ian Doust
Affiliation:
School of Mathematics, University of New South Wales, Kensington, NSW, 2033, Australia
Qiu Bozhou
Affiliation:
Department of Applied Mathematics, Tongji University, Shanghai, People's Republic of, China
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Abstract

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Well-bounded operators are those which possess a bounded functional calculus for the absolutely continuous functions on some compact interval. Depending on the weak compactness of this functional calculus, one obtains one of two types of spectral theorem for these operators. A method is given which enables one to obtain both spectral theorems by simply changing the topology used. Even for the case of well-bounded operators of type (B), the proof given is more elementary than that previously in the literature.

MSC classification

Secondary: 47B40: Spectral operators, decomposable operators, well-bounded operators, etc. 46A50: Compactness in topological linear spaces; angelic spaces, etc. 46H30: Functional calculus in topological algebras 47A60: Functional calculus
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 3 , June 1993 , pp. 334 - 351
Copyright
Copyright © Australian Mathematical Society 1993

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