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Sufficient conditions for a linear functional to be multiplicative |
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| Authors: | K Seddighi M H Shirdarreh Haghighi |
| Institution: | Department of Mathematics, Shiraz University, Shiraz 71454, Iran M. H. Shirdarreh Haghighi ; Department of Mathematics, Shiraz University, Shiraz 71454, Iran |
| Abstract: | A commutative Banach algebra |
| Keywords: | Multiplicative linear functional the $P(k n)$ property Banach algebra maximal ideal |
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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.