Remarks on homomorphisms on certain subalgebras of \(C(X)\). (English) Zbl 0798.46016

Biström, Peter; Bjon, Sten; Lindström, Mikael

Math. Jap. 37, No. 1, 105-109 (1992).

Let \(E\) be a real Hausdorff locally convex space. Then, the subject of the paper under review is to find conditions on \(E\) under which every non-zero homomorphism of \(C^ m(E)\) into \(\mathbb{R}\) is a point-evaluation at some point of \(E\). When \(E\) is a Banach space, results of this sort have been obtained by J. Arias-de-Reyna [Proc. Am. Math. Soc. 104, No. 4, 1054-1058 (1988; Zbl 0694.46036)] and others. Affirmative results are obtained for instance in the following cases:
(i) Lindelöf locally convex space,
(ii) Banach spaces whose dual is weak\(^*\)-separable,
(iii) the Mackey dual of a separable Fréchet space.

Reviewer: M.Hasumi (Mito / Ibaraki)

MSC:

46E25

Rings and algebras of continuous, differentiable or analytic functions

Keywords:

algebra of differentiable functions; homomorphism; point-evaluation; Lindelöf locally convex space; Banach spaces whose dual is weak\(^*\)- separable; Mackey dual of a separable Fréchet space

Citations:

Zbl 0694.46036