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Local derivations on c*-algebras are derivations

Lookup NU author(s): Professor Barry Johnson


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Kadison has shown that local derivations from a von Neumann algebra into any dual bimodule are derivations. In this paper we extend this result to local derivations from any C*-algebra into any Banach -bimodule X. Most of the work is involved with establishing this result when is a commutative C*-algebra with one self-adjoint generator. A known result of the author about Jordan derivations then completes the argument. We show that these results do not extend to the algebra C1[0, 1] of continuously differentiable functions on [0, 1], We also give an automatic continuity result, that is, we show that local derivations on C*-algebras are continuous even if not assumed a priori to be so. © 2000 American Mathematical Society.

Publication metadata

Author(s): Johnson BE

Publication type: Article

Publication status: Published

Journal: Transactions of the American Mathematical Society

Year: 2001

Volume: 353

Issue: 1

Pages: 313-325

Print publication date: 01/01/2001

ISSN (print): 0002-9947

ISSN (electronic): 1088-6850

Publisher: American Mathematical Society