## 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 $\mathcal {A}.$## References

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## Bibliographic 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
- Received by editor(s): December 6, 1995
- Received by editor(s) in revised form: June 12, 1996
- Communicated by: Palle E.T. Jorgensen
- © Copyright 1997 American Mathematical Society
- 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