Vol. 108, No. 1, 1983

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Topological properties of the dual pair (Ω),(Ω)′′

Peter Dierolf and Susanne Dierolf

Vol. 108 (1983), No. 1, 51–82
Abstract

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

Mathematical Subject Classification 2000
Primary: 46F05
Secondary: 46E10, 46A12
Milestones
Received: 8 October 1981
Published: 1 September 1983
Authors
Peter Dierolf
Susanne Dierolf