Vol. 85, No. 2, 1979

Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Compact and weakly compact derivations of Cāˆ—-algebras

Charles A. Akemann and Steve Wright

Vol. 85 (1979), No. 2, 253ā€“259
Abstract

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
Milestones
Received: 17 November 1978
Published: 1 December 1979
Authors
Charles A. Akemann
Steve Wright