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Compact actions on C*-algebras

Published online by Cambridge University Press:  18 May 2009

Charles A. Akemann  and
Steve Wright
Charles A. Akemann
Affiliation:
University Of California, Santa Barbara, California 93106
Steve Wright
Affiliation:
Oakland University, Rochester, Michigan 48063
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In Section 33 of [2], Bonsall and Duncan define an element t of a Banach algebra to act compactly on if the map a → tat is a compact operator on . In this paper, the arguments and technique of [1] are used to study this question for C*-algebras (see also [10]). We determine the elements b of a C*-algebra for which the maps a → ba, a → ab, a → ab + ba, a → bab are compact (respectively weakly compact), determine the C*-algebras which are compact in the sense of Definition 9, of [2, p. 177] and give a characterization of the C*-automorphisms of which are weakly compact perturbations of the identity.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 21 , Issue 2 , July 1980 , pp. 143 - 149
Copyright
Copyright © Glasgow Mathematical Journal Trust 1980

References

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