Weakly closed subspaces and the Hahn-Banach extension property in p-adic analysis. (English) Zbl 0678.46055

De Grande-De Kimpe, N.; Perez-Garcia, C.

Indag. Math. 50, No. 3, 253-261 (1988).

This paper contains a number of fine results in the theory of locally convex spaces over non-trivially valued non-archimedean fields which are not necessarily spherically complete.
The paper is closely related to recent work of W. H. Schikhof and K. U. Nijmegen [Bull. Soc. Math. Belg., Ser. B 38, 187-228 (1986; Zbl 0615.46071 and Zbl 0615.46072)] on polar and strongly polar spaces. New results are proved on the Hahn-Banach extension property, weak topologies, the weak extension property of continuous linear functionals defined on subspaces, weakly closed subspaces, convergent sequences and related subjects.

Reviewer: W.Govaerts

MSC:

46S10	Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
46A22	Theorems of Hahn-Banach type; extension and lifting of functionals and operators

Keywords:

locally convex spaces over non-trivially valued non-archimedean fields which are not necessarily spherically complete; strongly polar spaces; Hahn-Banach extension property; weak topologies; weak extension property of continuous linear functionals; weakly closed subspaces; convergent sequences

Citations:

Zbl 0615.46071; Zbl 0615.46072