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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Finite codimensional ideals in Banach algebras


Author: Krzysztof Jarosz
Journal: Proc. Amer. Math. Soc. 101 (1987), 313-316
MSC: Primary 46J05; Secondary 46J20
MathSciNet review: 902548
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Abstract: Let $ A$ be a commutative, selfadjoint, point spectral Banach algebra and let $ M$ be a finite codimensional closed subspace of $ A$ such that for each $ f$ in $ M$ there are $ n$ distinct maximal ideals $ I_1^f, \ldots ,I_n^f$ of $ A$ with $ f \in I_j^f$. We prove that then there are distinct maximal ideals $ {I_1}, \ldots ,{I_n}$ of $ A$ such that $ M \subset {I_1} \cap \cdots \cap {I_n}$; in particular if codim$ (M) = n$, then $ M$ is an ideal.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0902548-3
PII: S 0002-9939(1987)0902548-3
Article copyright: © Copyright 1987 American Mathematical Society