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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Linear maps preserving ideals of $C^{*}$-algebras


Author: Sang Og Kim
Journal: Proc. Amer. Math. Soc. 129 (2001), 1665-1668
MSC (2000): Primary 47B49
Published electronically: October 25, 2000
MathSciNet review: 1814095
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Abstract: We show that unital self-adjoint linear bijections of matrix algebras, type $II_{1}$ factors and abelian $C^{*}$-algebras preserving maximal left ideals are isomorphisms and we show that a unital continuous linear map of a $C^{*}$-algebra $A$ that maps the minimal left ideal $Ap$ into itself is the identity map.


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Additional Information

Sang Og Kim
Affiliation: Department of Mathematics, Hallym University, Chuncheon 200-702, Korea
Email: sokim@sun.hallym.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-00-06003-2
PII: S 0002-9939(00)06003-2
Keywords: $C^{*}$-algebra, derivation, minimal ideal
Received by editor(s): August 31, 1999
Published electronically: October 25, 2000
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2000 American Mathematical Society