J Austral Math Soc Ser A 54 pp334--351, 1993.

The Spectral Theorem for Well-Bounded Operators

Ian Doust and Qiu Bozhou

Abstract

Well-bounded operators are those which possess a bounded function calculus for the absolutely continuous functions on some compact interval. Depending on the weak compactness of this functional calculus, one obtains one or 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.

1991 AMS Subject Classification: primary 47B40; secondary 46A50, 46H30, 47A60

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Authors

Ian Doust

School of Mathematics, University of New South Wales, Kensington, NSW, 2033, Australia.

Qiu Bozhou

Department of Applied Mathematics, Tongji University, Shanghai, People's Republic of China.