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ArticleOriginal scientific text

Title

Two characterizations of automorphisms on B(X)

Authors 1

Affiliations

  1. Department of Mathematics, University of Ljubljana, Jadranska 19, 61000 Ljubljana, Slovenia

Abstract

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.

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Studia Mathematica
1993/105/2
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Pages:
143-149
Main language of publication
English
Received
1992-06-11
Accepted
1993-01-25
Published
1993
Exact and natural sciences