Nuclear spaces, Schauder bases, and Choquet simplexes

Aldo Joram Lazar and James Ronald Retherford

Vol. 37 (1971), No. 2, 409–419

DOI: 10.2140/pjm.1971.37.409

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