Vol. 85, No. 2, 1979

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Compact and weakly compact derivations of Cāˆ—-algebras

Charles A. Akemann and Steve Wright

Vol. 85 (1979), No. 2, 253ā€“259

In a forthcoming paper, the second-named author asks if every compact derivation of a C-algebra 𝒜 into a Banach 𝒜-module X is the uniform limit of flnite-rank derivations. We answer this question affirmatively in the present paper when X = 𝒜 by characterizing the structure of compact derivations of C-algebras. In addition, the structure of weakly compact derivations of C-algebras is determined, and as immediate corollaries of these results, necessary and sufficient conditions are given for a C-algebra to admit a nonzero compact or weakly compact derivation.

Mathematical Subject Classification 2000
Primary: 47B47
Secondary: 46L05
Received: 17 November 1978
Published: 1 December 1979
Charles A. Akemann
Steve Wright