Sufficient conditions for a linear functional to be multiplicative

Authors:
K. Seddighi and M. H. Shirdarreh Haghighi

Journal:
Proc. Amer. Math. Soc. **129** (2001), 2385-2393

MSC (2000):
Primary 46J20; Secondary 46J10

DOI:
https://doi.org/10.1090/S0002-9939-01-05720-3

Published electronically:
January 17, 2001

MathSciNet review:
1823923

Full-text PDF

Abstract | References | Similar Articles | Additional Information

A commutative Banach algebra is said to have the property if the following holds: Let be a closed subspace of finite codimension such that, for every , the Gelfand transform has at least distinct zeros in , the maximal ideal space of . Then there exists a subset of of cardinality such that vanishes on , the set of common zeros of . In this paper we show that if is compact and nowhere dense, then , the uniform closure of the space of rational functions with poles off , has the property for all . We also investigate the property for the algebra of real continuous functions on a compact Hausdorff space.

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Additional Information

**K. Seddighi**

Affiliation:
Department of Mathematics, Shiraz University, Shiraz 71454, Iran

**M. H. Shirdarreh Haghighi**

Affiliation:
Department of Mathematics, Shiraz University, Shiraz 71454, Iran

Email:
shir@sun01.susc.ac.ir

DOI:
https://doi.org/10.1090/S0002-9939-01-05720-3

Keywords:
Multiplicative linear functional,
the $P(k,n)$ property,
Banach algebra,
maximal ideal

Received by editor(s):
January 31, 1999

Received by editor(s) in revised form:
December 17, 1999

Published electronically:
January 17, 2001

Additional Notes:
This research was partially supported by a grant from IPM, The Institute for Studies in Theoretical Physics and Mathematics.

Communicated by:
David R. Larson

Article copyright:
© Copyright 2001
American Mathematical Society