A dual geometric characterization of Banach spaces not containing<i>l</i>₁

Abstract

It is shown that a Banach space E does not contain a copy of /, if and only if every bounded subset of E* is w*-deniable in ("*, (*, **)). The notion of w*-scalarly deniable sets in dual Banach space is introduced and it is proved that a Banach space E does not contain a copy of /, 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 /,, is given.