On 2-local *-automorphisms and 2-local isometries of B(H)

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Abstract

It is an important result of Šemrl which states that every 2-local automorphism of the full operator algebra over a separable Hilbert space is necessarily an automorphism. In this paper we strengthen that result quite substantially for *-automorphisms. Indeed, we show that one can compress the defining two equations of 2-local *-automorphisms into one single equation, hence weakening the requirement significantly, but still keeping essentially the conclusion that such maps are necessarily *-automorphisms.

Original languageEnglish
JournalJournal of Mathematical Analysis and Applications
DOIs
Publication statusPublished - Jan 1 2019

Keywords

  • *-Automorphisms
  • 2-Local maps
  • Algebra of Hilbert space operators
  • Surjective isometries

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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