Local automorphisms of operator algebras on Banach spaces
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Abstract:
In this paper we extend a result of Šemrl 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 Šemrl’s paper.References
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Additional Information
- Lajos Molnár
- Affiliation: Institute of Mathematics and Informatics, University of Debrecen, 4010 Debrecen, P.O. Box 12, Hungary
- Email: molnarl@math.klte.hu
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1867-1874
- MSC (2000): Primary 47B49, 16S50
- DOI: https://doi.org/10.1090/S0002-9939-02-06786-2
- MathSciNet review: 1955275