Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

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

Author(s): Sang Og Kim
Journal: Proc. Amer. Math. Soc. 129 (2001), 1665-1668.
MSC (2000): Primary 47B49
Posted: 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 that maps the minimal left ideal into itself is the identity map.

References:

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5.: E. Størmer, On the Jordan structure of $C^{*}$ -algebras, Trans. Amer. Math. Soc. 120 (1965), 438-447. MR 32:2930

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