Finite codimensional ideals in function algebras

Jarosz, Krzysztof

doi:10.1090/S0002-9947-1985-0768740-9

Finite codimensional ideals in function algebras
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by Krzysztof Jarosz

Trans. Amer. Math. Soc. 287 (1985), 779-785

DOI: https://doi.org/10.1090/S0002-9947-1985-0768740-9

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Abstract:

Assume $S$ is a compact, metric space and let $M$ be a finite codimensional closed subspace of a complex space $C(S)$. In this paper we prove that if each element from $M$ has at least $k$ zeros in $S$, then for some ${s_1}, \ldots ,{s_k} \in S,M \subseteq \{ f \in C(S):f({s_1}) = \cdots = f({s_k}) = 0\}$.

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