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

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that a C-algebra is prime iff for every where denotes Taylor spectrum and are the left and right multiplication operators acting on

**[Cu1]**R. Curto, Applications of several complex variables to multiparameter spectral theory, Surveys of Some Recent Results in Operator Theory, J.B. Conway and B. Morrel, eds., vol. II, Pitman Res. Notes in Math. Ser. 192, Longman Publ. Co., London, 1988; pp. 25-90. MR**90d:47007****[Cu2]**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****[CuF]**R. Curto and L. Fialkow, The spectral picture of J. Funct. Anal. 71(1987), 371-392. MR**88c:47006****[Har]**R. Harte, A problem of mixed interpolation, Math. Z. 143(1975), 149-153. MR**53:8933****[Ma1]**M. Mathieu, Applications of ultraprime Banach algebras in the theory of elementary operators, Thesis, Univ. Tübingen, 1986.**[Ma2]**M. Mathieu, Elementary operators on prime C-algebras, I, Math. Ann. 284(1989), 223-244. MR**90h:46092****[Ta1]**J.L. Taylor, A joint spectrum for several commuting operators, J. Funct. Anal. 6(1970), 172-191. MR**42:3603****[Ta2]**J.L. Taylor, The analytic functional calculus for several commuting operators, Acta Math. 125(1970), 1-38. MR**42:6622**

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

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

Article copyright:
© Copyright 1997
American Mathematical Society