Vol. 105, No. 2, 1983

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ISSN: 0030-8730
A dual geometric characterization of Banach spaces not containing l1

Elias Saab and Paulette Saab

Vol. 105 (1983), No. 2, 415–425
Abstract

It is shown that a Banach space E does not contain a copy of l1 if and only if every bounded subset of E is w-dentable in (E(E,E∗∗)). The notion of w-scalarly dentable sets in dual Banach space is introduced and it is proved that a Banach space E does not contain a copy of l1 if and only if every bounded set in E is w-scalarly dentable. Finally, a point of continuity criterion that characterizes Asplund operators and those operators that factor through Banach spaces not containing copies of l1, is given.

Mathematical Subject Classification 2000
Primary: 46B20
Milestones
Received: 23 September 1981
Published: 1 April 1983
Authors
Elias Saab
Paulette Saab