Proceedings of the American Mathematical Society

Author(s): Lajos Molnár
Journal: Proc. Amer. Math. Soc. 131 (2003), 1867-1874.
MSC (2000): Primary 47B49, 16S50
Posted: November 6, 2002
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B49, 16S50

Lajos Molnár
Affiliation: Institute of Mathematics and Informatics, University of Debrecen, 4010 Debrecen, P.O. Box 12, Hungary
Email: molnarl@math.klte.hu

DOI: 10.1090/S0002-9939-02-06786-2
PII: S 0002-9939(02)06786-2
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
Posted: 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
Copyright of article: Copyright 2002, American Mathematical Society

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