Vol. 84, No. 1, 1979

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A density result in spaces of Silva holomorphic mappings

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

Vol. 84 (1979), No. 1, 35–42

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,F)0) of holomorphic functions on Ω with values in a locally convex space F is a dense topological subspace of (HS,F)so), the space of Silva holomorphic functions endowed with the strictly compact open topology. This is used to give a certain bidual interpretation for (HS,F)so), if F is a complete Schwartz locally convex space.

Mathematical Subject Classification 2000
Primary: 46G20
Secondary: 32E30, 46A12
Received: 29 November 1977
Revised: 8 February 1979
Published: 1 September 1979
J.-F. Colombeau
Reinhold Meise
Bernard Perrot