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Positive Linear Mappings Between C*-Algebras

Published online by Cambridge University Press:  20 November 2018

Yong Zhong
Yong Zhong*
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 1A1, e-mail:zhong@math.toronto.edu
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Abstract

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We prove that a positive unital linear mapping from a von Neumann algebra to a unital C*-algebra is a Jordan homomorphism if it maps invertible selfadjoint elements to invertible elements, and that for any compact Hausdorff space X, all positive unital linear mappings from C(X) into a unital C*-algebra that preserve the invertibility for self-adjoint elements are *-homomorphisms if and only if X is totally disconnected.

Keywords

46L0546J10C*-algebraJordan homomorphismtotally disconnected space
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 2 , 01 June 1995 , pp. 252 - 256
Copyright
Copyright © Canadian Mathematical Society 1995

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