The range of a ring homomorphism

from a commutative -algebra

Author:
Lajos Molnár

Journal:
Proc. Amer. Math. Soc. **124** (1996), 1789-1794

MSC (1991):
Primary 46J05, 46E25

DOI:
https://doi.org/10.1090/S0002-9939-96-03236-4

MathSciNet review:
1307551

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Abstract: We prove that if a commutative semi-simple Banach algebra is the range of a ring homomorphism from a commutative -algebra, then is -equivalent, i.e. there are a commutative -algebra and a bicontinuous algebra isomorphism between and . In particular, it is shown that the group algebras , and the disc algebra are not ring homomorphic images of -algebras.

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Additional Information

**Lajos Molnár**

Affiliation:
Institute of Mathematics, Lajos Kossuth University, 4010 Debrecen, P.O.Box 12, Hungary

Email:
molnarl@math.klte.hu

DOI:
https://doi.org/10.1090/S0002-9939-96-03236-4

Keywords:
Ring homomorphism,
commutative Banach algebra,
Gelfand representation

Received by editor(s):
November 21, 1994

Additional Notes:
Research partially supported by the Hungarian National Research Science Foundation, Operating Grant Number OTKA 1652 and K&H Bank Ltd., Universitas Foundation.

Communicated by:
Palle E. T. Jorgensen

Article copyright:
© Copyright 1996
American Mathematical Society