Local automorphisms of operator algebras on Banach spaces

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32 Citations (Scopus)

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 Hubert space is an automorphism. In fact, besides separable Hubert 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.

Original languageEnglish
Pages (from-to)1867-1874
Number of pages8
JournalProceedings of the American Mathematical Society
Volume131
Issue number6
DOIs
Publication statusPublished - Jun 2003

Keywords

  • Automorphism
  • Local automorphism
  • Matrix algebra
  • Operator algebra

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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