The Mackey-Arens theorem for non-locally convex spaces. (English) Zbl 0745.46009

Kakol, Jerzy

Collect. Math. 41, No. 2, 129-132 (1990).

Summary: Let \({\mathcal R}\) be a subcategory of the category of all topological vector spaces. Let \(E\in{\mathcal R}\). The problem of the existence of the finest \({\mathcal R}\)-topology on \(E\) with the same continuous linear functions as the original one is discussed. Remarks concerning the Hahn-Banach extension property are included.

MSC:

46A16

Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.)

Keywords:

Mackey-Arens theorem for nonlocally convex spaces; Hahn-Banach extension property