A real valued homomorphism on algebras of differentiable functions

Abstract:

In this paper we prove that, for every homomorphism $A$ on ${C^k}\left ( E \right )$, there exists $x \in E$ such that $A\left ( f \right ) = f\left ( x \right )$ for $f \in {C^k}\left ( E \right )$. Here ${C^k}\left ( E \right )\;\left ( {k = 1,2, \ldots , \infty } \right )$ denotes the algebra of all $k$-times differentiable real functions on a real and separable Banach space $E$.