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2-LOCAL ISOMETRIES OF SOME OPERATOR ALGEBRAS

Published online by Cambridge University Press:  17 June 2002

Lajos Molnár
Lajos Molnár
Affiliation:
Institute of Mathematics and Informatics, University of Debrecen, 4010 Debrecen, PO Box 12, Hungary ([email protected])
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Abstract

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As a consequence of the main result of the paper we obtain that every 2-local isometry of the $C^*$-algebra $B(H)$ of all bounded linear operators on a separable infinite-dimensional Hilbert space $H$ is an isometry. We have a similar statement concerning the isometries of any extension of the algebra of all compact operators by a separable commutative $C^*$-algebra. Therefore, on those $C^*$-algebras the isometries are completely determined by their local actions on the two-point subsets of the underlying algebras.

AMS 2000 Mathematics subject classification: Primary 47B49

Keywords

operator algebraisometrylocal isometry
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 2 , June 2002 , pp. 349 - 352
Copyright
Copyright © Edinburgh Mathematical Society 2002