Vol. 108, No. 1, 1983

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An ordering for the Banach spaces

Gerald Arthur Edgar

Vol. 108 (1983), No. 1, 83–98

A binary relation will be defined on the class of all Banach spaces. The relation is transitive and symmetric, so it is natural to call it an “ordering”. (The definition also makes sense for locally convex spaces with good duality properties, but this will not be pursued here.) Many of the elementary properties of the ordering are spelled out. Although some connections with Pettis integration and unique preduals have been found, the usefulness of this ordering in Banach space theory remains to be determined.

Mathematical Subject Classification 2000
Primary: 46B20
Secondary: 46G10, 46M99
Received: 16 December 1981
Revised: 8 March 1982
Published: 1 September 1983
Gerald Arthur Edgar