A Banach-Dieudonné theorem for the space of bounded continuous functions on a separable metric space with the strict topology

A Banach-Dieudonné theorem for the space of bounded continuous functions on a separable metric space with the strict topology

Kraaij, R.C. (TU Delft Applied Probability)

2016-08-15

Let X be a separable metric space and let β be the strict topology on the space of bounded continuous functions on X, which has the space of τ-additive Borel measures as a continuous dual space. We prove a Banach-Dieudonné type result for the space of bounded continuous functions equipped with β: the finest locally convex topology on the dual space that coincides with the weak topology on all weakly compact sets is a k-space. As a consequence, the space of bounded continuous functions with the strict topology is hypercomplete and a Pták space. Additionally, the closed graph, inverse mapping and open mapping theorems holds for linear maps between space of this type.

Banach-Dieudonné theorem
Closed graph theorem
Space of bounded continuous functions
Strict topology

http://resolver.tudelft.nl/uuid:47e2885d-581f-4185-9b51-b1e3dc7dab4e

https://doi.org/10.1016/j.topol.2016.06.003

0166-8641

Topology and Its Applications: a journal devoted to general, geometric, set-theoretic and algebraic topology, 209, 181-188

Institutional Repository

journal article

© 2016 R.C. Kraaij