Closed subspaces of finite codimension in some function algebras

Garimella, Ramesh V.; Rao, N. V.

doi:10.1090/S0002-9939-1987-0911028-0

Closed subspaces of finite codimension in some function algebras
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by Ramesh V. Garimella and N. V. Rao

Proc. Amer. Math. Soc. 101 (1987), 657-661

DOI: https://doi.org/10.1090/S0002-9939-1987-0911028-0

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Abstract:

We characterize all closed subspaces of finite codimension in some specific types of function algebras e.g. these include $C(X)$: algebra of continous functions on a compact Hausdorff space, ${C^n}[a,b]$: the algebra of $n$-times continuously differentiable functions on the closed interval $[a,b]$. Our work is a generalization of the well-known Gleason-Kahane-Želazko theorem [3, 6] for subspaces of codimension one in arbitrary unitary Banach algebras.

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