# zbMATH — the first resource for mathematics

Weak sequential convergence and weak compactness in spaces of vector-valued continuous functions. (English) Zbl 0854.46032
Let $$X$$ be a completely regular Hausdorff space, $$E$$ be a Hausdorff locally convex space and $$C_b (X, E)$$ be the space of all bounded continuous $$E$$-valued functions on $$X$$. The necessary and sufficient conditions that a sequence $$(f_n)$$ of elements of $$C_b (X, E)$$ would be weakly convergent to zero in $$(C_b (X, E), \tau)$$ and a subset $$H\subset C_b (X, E)$$ would be weakly relatively (countably) compact in $$(C_b (X, E), \tau)$$ are given in the case, when $$\tau$$ is one of the strict topologies defined on $$C_b (X, E)$$.
Reviewer: M.Abel (Tartu)

##### MSC:
 4.6e+41 Spaces of vector- and operator-valued functions 4.6e+11 Topological linear spaces of continuous, differentiable or analytic functions
Full Text: