Multiplicative functionals on algebras of differentiable functions
For a class of Banach spaces E including separable spaces and realcompact super-reflexive spaces, it is shown in this note that every nonzero scalar homomorphism on the algebra \(C^ m(\Omega)\) of all \(C^ m\)- functions defined on an open subset \(\Omega\) of E is given by evaluation at some point of \(\Omega\).
multiplicative functionals on algebras of differentiable functions
scientific article; zbMATH DE number 4198806
scientific article