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ArticleOriginal scientific text

Title

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

Authors 1

Affiliations

  1. Institute of Mathematics, Lajos Kossuth University, P.O. Box 12, 4010 Debrecen, Hungary

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)=limnΦn(A). Then Φ is an automorphism. Moreover, a similar statement holds for the set of all surjective isometries of B(H).

Keywords

ENG
reflexivity, automorphism, Jordan homomorphism, automatic surjectivity

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Studia Mathematica
1997/122/2
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Pages:
183-193
Main language of publication
English
Received
1996-04-02
Accepted
1996-09-06
Published
1997
Exact and natural sciences