Local automorphisms and derivations on

Author:
Peter Semrl

Journal:
Proc. Amer. Math. Soc. **125** (1997), 2677-2680

MSC (1991):
Primary 47B47

DOI:
https://doi.org/10.1090/S0002-9939-97-04073-2

MathSciNet review:
1415338

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an algebra. A mapping is called a -local automorphism if for every there is an automorphism , depending on and , such that and (no linearity, surjectivity or continuity of is assumed). Let be an infinite-dimensional separable Hilbert space, and let be the algebra of all linear bounded operators on . Then every -local automorphism is an automorphism. An analogous result is obtained for derivations.

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Additional Information

**Peter Semrl**

Affiliation:
Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, 2000 Maribor, Slovenia

Email:
peter.semrl@uni-mb.si

DOI:
https://doi.org/10.1090/S0002-9939-97-04073-2

Received by editor(s):
April 19, 1996

Additional Notes:
This work was supported by a grant from the Ministry of Science of Slovenia

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1997
American Mathematical Society