Linear maps preserving ideals of 𝐶*-algebras

Kim, Sang

doi:10.1090/S0002-9939-00-06003-2

Linear maps preserving ideals of $C^{*}$-algebras
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by Sang Og Kim PDF

Proc. Amer. Math. Soc. 129 (2001), 1665-1668 Request permission

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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