FS-property for 𝐶*-algebras

Kodaka, Kazunori; Osaka, Hiroyuki

doi:10.1090/S0002-9939-00-05712-9

FS-property for $C^*$-algebras
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by Kazunori Kodaka and Hiroyuki Osaka PDF

Proc. Amer. Math. Soc. 129 (2001), 999-1003 Request permission

Abstract:

A $C^{\ast }$-algebra $A$ is said to have the FS-property if the set of all self-adjoint elements in $A$ has a dense subset of elements with finite spectrum. We shall show that this property is not stable under taking the minimal $C^{\ast }$-tensor products even in case of separable nuclear $C^{\ast }$-algebras.

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