Sufficient conditions for a linear functional to be multiplicative
Authors:
K. Seddighi and M. H. Shirdarreh Haghighi
Journal:
Proc. Amer. Math. Soc. 129 (2001), 23852393
MSC (2000):
Primary 46J20; Secondary 46J10
Published electronically:
January 17, 2001
MathSciNet review:
1823923
Fulltext PDF Free Access
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Abstract: 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:
http://dx.doi.org/10.1090/S0002993901057203
PII:
S 00029939(01)057203
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
