A density result in spaces of Silva holomorphic mappings

J.-F. Colombeau, Reinhold Meise and Bernard Perrot

Vol. 84 (1979), No. 1, 35–42

DOI: 10.2140/pjm.1979.84.35

Abstract

A modification of an idea of Aron and Schottenloher is used to show: For any finitely Runge open subset Ω in certain locally convex spaces E (including the class of quasicomplete dualnuclear spaces) the space (H(Ω,F),τ₀) of holomorphic functions on Ω with values in a locally convex space F is a dense topological subspace of (H_S(Ω,F),τ_so), the space of Silva holomorphic functions endowed with the strictly compact open topology. This is used to give a certain bidual interpretation for (H_S(Ω,F),τ_so), if F is a complete Schwartz locally convex space.

Mathematical Subject Classification 2000

Primary: 46G20

Secondary: 32E30, 46A12

Milestones

Received: 29 November 1977

Revised: 8 February 1979

Published: 1 September 1979