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Local automorphisms of operator algebras on Banach spaces

Author: Lajos Molnár
Journal: Proc. Amer. Math. Soc. 131 (2003), 1867-1874
MSC (2000): Primary 47B49, 16S50
Published electronically: November 6, 2002
MathSciNet review: 1955275
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Abstract: In this paper we extend a result of Semrl stating that every 2-local automorphism of the full operator algebra on a separable infinite dimensional Hilbert space is an automorphism. In fact, besides separable Hilbert spaces, we obtain the same conclusion for the much larger class of Banach spaces with Schauder bases. The proof rests on an analogous statement concerning the 2-local automorphisms of matrix algebras for which we present a short proof. The need to get such a proof was formulated in Semrl's paper.

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Additional Information

Lajos Molnár
Affiliation: Institute of Mathematics and Informatics, University of Debrecen, 4010 Debrecen, P.O. Box 12, Hungary

Keywords: Automorphism, local automorphism, matrix algebra, operator algebra
Received by editor(s): November 22, 2000
Received by editor(s) in revised form: February 6, 2002
Published electronically: November 6, 2002
Additional Notes: This research was supported by the Hungarian National Foundation for Scientific Research (OTKA), Grant No. T030082, T031995, and by the Ministry of Education, Hungary, Reg. No. FKFP 0349/2000
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society