The structure of homomorphisms from Banach algebras of differentiable functions into finite dimensional Banach algebras (Q804908)

Let \(n\in N\) and \(C^ n[0,1]\) be the Banach algebra of n time continuously differentiable functions on the unit interval. It is shown that every continuous and every discontinuous homomorphism \(\nu\) of \(C^ n[0,1]\) onto a finite dimensional local algebra with hull(ker \(\nu\))\(=\{0\}\) is completely determined by higher point derivations of functions of \(C^ n[0,1]\).