Local derivations on -algebras are derivations

Author:
B. E. Johnson

Journal:
Trans. Amer. Math. Soc. **353** (2001), 313-325

MSC (2000):
Primary 46L57, 46H40

Published electronically:
September 18, 2000

MathSciNet review:
1783788

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Abstract | References | Similar Articles | Additional Information

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 -algebra into any Banach -bimodule . Most of the work is involved with establishing this result when is a commutative -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 of continuously differentiable functions on . We also give an automatic continuity result, that is, we show that local derivations on -algebras are continuous even if not assumed a priori to be so.

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Additional Information

**B. E. Johnson**

Affiliation:
Department of Mathematics, University of Newcastle, Newcastle upon Tyne, England NE1 7RU

Email:
b.e.johnson@ncl.ac.uk

DOI:
https://doi.org/10.1090/S0002-9947-00-02688-X

Received by editor(s):
June 24, 1999

Published electronically:
September 18, 2000

Article copyright:
© Copyright 2000
American Mathematical Society