Topological properties of the dual pair ⟨ℬ(Ω)^′,ℬ(Ω)^′′⟩

Peter Dierolf and Susanne Dierolf

Vol. 108 (1983), No. 1, 51–82

DOI: 10.2140/pjm.1983.108.51

Abstract

If Ω≠∅ is an open subset of Rⁿ, various locally convex topologies have been proposed that make the bidual ℬ(Ω)′′ a normal space of distributions with dual ℬ′. It is shown that these topologies all coincide; in particular, the strict topology on ℬ(Ω)′′ is a Mackey topology. Moreover, the dual ℬ(Ω)′ has the Schur property, and ℬ(Ω)′′ is an Orlicz-Pettis space.

Mathematical Subject Classification 2000

Primary: 46F05

Secondary: 46E10, 46A12

Milestones

Received: 8 October 1981

Published: 1 September 1983