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Automatic Continuity of Separating Linear Isomorphisms

Published online by Cambridge University Press:  20 November 2018

Krzysztof Jarosz
Krzysztof Jarosz*
Affiliation:
Institute of Mathematics, Warsaw University, 00-901 Warsaw, PKiN9p., Poland and Department of Mathematics and Statistics, Southern Illinois University, Edwardsville, Il. 62026, U.S.A.
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Abstract

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A linear map A : C(T) → C(S) is called separating if f • g ≡ 0 implies Af • Ag = 0. We describe the general form of such maps and prove that any separating isomorphism is continuous.

Keywords

46E15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 2 , 01 June 1990 , pp. 139 - 144
Copyright
Copyright © Canadian Mathematical Society 1990

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