A joint spectral characterization of primeness for C*-algebras

Curto, Raúl; G., Carlos

doi:10.1090/S0002-9939-97-03948-8

A joint spectral characterization of primeness for C$^*$-algebras
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by Raúl E. Curto and Carlos Hernández G.

Proc. Amer. Math. Soc. 125 (1997), 3299-3301

DOI: https://doi.org/10.1090/S0002-9939-97-03948-8

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Abstract:

We prove that a C$^{*}$-algebra $\mathcal {A}$ is prime iff $\sigma _T((L_a,R_b),\mathcal {A}) =\sigma (a)\times \sigma (b)$ for every $a,b\in \mathcal {A},$ where $\sigma _T$ denotes Taylor spectrum and $L_a,R_b$ are the left and right multiplication operators acting on $\mathcal {A}.$

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