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Linear Maps on Factors which Preserve the Extreme Points of the Unit Ball

Published online by Cambridge University Press:  20 November 2018

Vania Mascioni  and
Lajos Molnár
Vania Mascioni
Affiliation:
Department of Mathematics The University of Texas at Austin Austin, Texas 78712 U.S.A., e-mail: mascioni@math.utexas.edu
Lajos Molnár
Affiliation:
Institute of Mathematics Lajos Kossuth University P.O. Box 12 4010 Debrecen Hungary, e-mail: molnarl@math.klte.hu
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Abstract

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The aim of this paper is to characterize those linear maps from a von Neumann factor $A$ into itself which preserve the extreme points of the unit ball of $A$. For example, we show that if $A$ is infinite, then every such linear preserver can be written as a fixed unitary operator times either a unital *-homomorphism or a unital $*$-antihomomorphism.

Keywords

47B4947D25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 41 , Issue 4 , 01 December 1998 , pp. 434 - 441
Copyright
Copyright © Canadian Mathematical Society 1998

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