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FS-property for -algebras
Authors:Kazunori Kodaka  Hiroyuki Osaka
Institution:Department of Mathematical Sciences, Faculty of Science, Ryukyu University, Nishi- hara-cho, Okinawa 903-0213, Japan ; Department of Mathematics, Ritsumeikan University, Kusatsu, Shiga, 525-8577, Japan
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.

Keywords:$C^*$-algebras  FS-property  K-groups  real rank
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