Acta Mathematica Sinica, English Series

, Volume 33, Issue 4, pp 545–553 | Cite as

Super weak compactness and uniform Eberlein compacta

Article

Abstract

We prove that a topological space is uniform Eberlein compact iff it is homeomorphic to a super weakly compact subset C of a Banach space such that the closed convex hull co̅C of C is super weakly compact. We also show that a Banach space X is super weakly compactly generated iff the dual unit ball BX* of X* in its weak star topology is affinely homeomorphic to a super weakly compactly convex subset of a Banach space.

Keywords

Banach space uniform Eberlein compactas super weak compactness 

MR(2010) Subject Classification

46B20 46B50 

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesDalian University of TechnologyDalianP. R. China
  2. 2.School of Mathematical SciencesQinzhou UniversityQinzhouP. R. China
  3. 3.School of Mathematical SciencesXiamen UniversityXiamenP. R. China

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