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 | 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]**Raúl E. Curto,*Applications of several complex variables to multiparameter spectral theory*, Surveys of some recent results in operator theory, Vol. II, Pitman Res. Notes Math. Ser., vol. 192, Longman Sci. Tech., Harlow, 1988, pp. 25–90. MR**976843****[Cu2]**Raúl E. Curto,*Spectral theory of elementary operators*, Elementary operators and applications (Blaubeuren, 1991) World Sci. Publ., River Edge, NJ, 1992, pp. 3–52. MR**1183936****[CuF]**Raúl E. Curto and Lawrence A. Fialkow,*The spectral picture of (𝐿_{𝐴},𝑅_{𝐵})*, J. Funct. Anal.**71**(1987), no. 2, 371–392. MR**880986**, 10.1016/0022-1236(87)90010-3**[Har]**Robin E. Harte,*A problem of mixed interpolation*, Math. Z.**143**(1975), no. 2, 149–153. MR**0405138****[Ma1]**M. Mathieu, Applications of ultraprime Banach algebras in the theory of elementary operators, Thesis, Univ. Tübingen, 1986.**[Ma2]**Martin Mathieu,*Elementary operators on prime 𝐶*-algebras. I*, Math. Ann.**284**(1989), no. 2, 223–244. MR**1000108**, 10.1007/BF01442873**[Ta1]**Joseph L. Taylor,*A joint spectrum for several commuting operators*, J. Functional Analysis**6**(1970), 172–191. MR**0268706****[Ta2]**Joseph L. Taylor,*The analytic-functional calculus for several commuting operators*, Acta Math.**125**(1970), 1–38. MR**0271741**

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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