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Compact actions on C*-algebras
Published online by Cambridge University Press: 18 May 2009
Extract
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.
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- Copyright © Glasgow Mathematical Journal Trust 1980
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