Two characterizations of automorphisms on B(X)

• Autorzy: Peter Šemrl
• Języki publikacji: EN

Abstrakty

EN

Let X be an infinite-dimensional Banach space, and let ϕ be a surjective linear map on B(X) with ϕ(I) = I. If ϕ preserves injective operators in both directions then ϕ is an automorphism of the algebra B(X). If X is a Hilbert space, then ϕ is an automorphism of B(X) if and only if it preserves surjective operators in both directions.

Kategorie tematyczne

• 47B49: Transformers, preservers (operators on spaces of operators)
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 105
• Numer: 2
• Strony: 143-149

Daty

wydano

1993

otrzymano

1992-06-11

poprawiono

1993-01-25

Twórcy

autor

Peter Šemrl

• Department of Mathematics, University of Ljubljana, Jadranska 19, 61000 Ljubljana, Slovenia

Bibliografia

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