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

• Autorzy: Lajos Molnár
• Języki publikacji: EN

Abstrakty

EN

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 $(Φ_n)$ of automorphisms of B(H) (depending on A) such that $Φ(A)= lim_n Φ_n(A)$. Then Φ is an automorphism. Moreover, a similar statement holds for the set of all surjective isometries of B(H).

Słowa kluczowe

EN

reflexivity; automorphism; Jordan homomorphism; automatic surjectivity

Kategorie tematyczne

• 47B49: Transformers, preservers (operators on spaces of operators)
• 46L40: Automorphisms

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 122
• Numer: 2
• Strony: 183-193

Daty

wydano

1997

otrzymano

1996-04-02

poprawiono

1996-09-06

Twórcy

autor

Lajos Molnár

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

Bibliografia

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