The set of automorphisms of B(H) is topologically reflexive in B(B(H))

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Abstract

The aim of this paper is to prove the statement announced in the title which can be reformulated in the following way. Let H be a separable infinite-dimensional Hilbert space and let Φ : B(H) → B(H) be a continuous linear mapping with the property that for every A ∈ B(H) there exists a sequence (Φn) of automorphisms of B(H) (depending on A) such that Φ(A) = limn Φn(A). Then Φ is an automorphism. Moreover, a similar statement holds for the set of all surjective isometries of B(H).

Original languageEnglish
Pages (from-to)183-193
Number of pages11
JournalStudia Mathematica
Volume122
Issue number2
DOIs
Publication statusPublished - Jan 1 1997

Keywords

  • Automatic surjectivity
  • Automorphism
  • Jordan homomorphism
  • Reflexivity

ASJC Scopus subject areas

  • Mathematics(all)

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