Vol. 37, No. 2, 1971

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Nuclear spaces, Schauder bases, and Choquet simplexes

Aldo Joram Lazar and James Ronald Retherford

Vol. 37 (1971), No. 2, 409–419
Abstract

We prove that a Frechet space E with a Schauder basis is nuclear if and only if every bounded subset of E is contained in a bounded Choquet simplex. We then show how this theorem relates to the basis problem for nuclear Frechet spaces and to the classical Banach-Dieudonné theorem.

Mathematical Subject Classification 2000
Primary: 46A35
Secondary: 46A15
Milestones
Received: 13 January 1971
Published: 1 May 1971
Authors
Aldo Joram Lazar
James Ronald Retherford