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A joint spectral characterization
of primeness for C$^{*}$-algebras

Authors: Raúl E. Curto and Carlos Hernández G.
Journal: Proc. Amer. Math. Soc. 125 (1997), 3299-3301
MSC (1991): Primary 46L05, 47A10, 47A13, 47C15, 47D25; Secondary 47A62, 18G35
MathSciNet review: 1403120
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Abstract: We prove that a C$^{*}$-algebra $\mathcal {A}$ is prime iff $\sigma _T((L_a,R_b),\mathcal {A})\break =\sigma (a)\times \sigma (b)$ 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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Additional Information

Raúl E. Curto
Affiliation: Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242

Carlos Hernández G.
Affiliation: Instituto de Matemáticas, UNAM, Ciudad Universitaria, 04510 Mexico, D.F., Mexico

Keywords: Taylor spectrum, multiplication operators, prime C$^{*}$-algebras
Received by editor(s): December 6, 1995
Received by editor(s) in revised form: June 12, 1996
Communicated by: Palle E.T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society