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Linear maps on factors which preserve the extreme points of the unit ball |
Canad. Math. Bull. 41(1998), 434-441
Published:1998-12-01
Printed: Dec 1998
Printed: Dec 1998
- Vania Mascioni
- Lajos Molnár
Abstract
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 $\ast$-homomorphism or a unital
$\ast$-antihomomorphism.
| MSC Classifications: |
47B49 - Transformers, preservers (operators on spaces of operators) 47D25 - unknown classification 47D25 |