Closed subspaces of finite codimension in some function algebras

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.