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

Author(s): Raúl E. Curto; Carlos Hernández G.
Journal: Proc. Amer. Math. Soc. 125 (1997), 3299-3301.
MSC (1991): Primary 46L05, 47A10, 47A13, 47C15, 47D25; Secondary 47A62, 18G35
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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 $\mathcal {A}.$

References:

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R. Curto, Spectral theory of elementary operators, Proceedings of the International Workshop on Elementary Operators and Applications, M. Mathieu, ed., World Scientific, 1992; pp. 3-52. MR 93i:47041

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Additional Information:

Raúl E. Curto
Affiliation: Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242
Email: curto@math.uiowa.edu

Carlos Hernández G.
Affiliation: Instituto de Matemáticas, UNAM, Ciudad Universitaria, 04510 Mexico, D.F., Mexico
Email: carlosh@servidor.unam.mx

DOI: 10.1090/S0002-9939-97-03948-8
PII: S 0002-9939(97)03948-8
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
Copyright of article: Copyright 1997, American Mathematical Society

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