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
DOI:
https://doi.org/10.1090/S0002-9939-97-03948-8
MathSciNet review:
1403120
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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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Additional Information
Raúl E. Curto
Affiliation:
Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242
MR Author ID:
53500
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
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
