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Elementary operators on prime C*-algebras II†

Published online by Cambridge University Press:  18 May 2009

Martin Mathieu
Martin Mathieu
Affiliation:
Mathematisches Institut der, Universitat Tübingen, 7400 Tübingen, West Germany
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Compact elementary operators acting on the algebra ℒ(H) of all bounded operators on some Hilbert space H were characterised by Fong and Sourour in [9]. Akemann and Wright investigated compact and weakly compact derivations on C*-algebras [1], and also studied compactness properties of the sum and the product of the right and the left regular representation of an element in a C*-algebra [2]. They used the concept of a compact Banach algebra element due to Vala [17]: an element a in a Banach algebra A is called compact if the mapping x → axa is compact on A. This notion has been further investigated by Ylinen [18, 19, 20], who showed in particular that a is a compact element of the C*-algebra A if x ↦ axa is weakly compact on A [19].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 3 , September 1988 , pp. 275 - 284
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

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