Rendiconti del Circolo Matematico di Palermo

, Volume 50, Issue 3, pp 455–476 | Cite as

Finitely purely atomic measures: Coincidence and rigidity properties

  • Ion Chiţescu
Article

Abstract

This paper is a natural continuation of the paper [2] by the same author.

We shall prove that several coincidence and rigidity phenomena which usually do not appear are possible only in case the underlying measure space is trivial (i.e. is a finite union of atoms). Examples: coincidence of twoL p spaces, reflexivity ofL 1, Radon—Nikodym property ofL , coincidence of Dunford, Pettis or Bochner integrability, coincidence of theL p space and of the weakL p space.

Keywords

Banach Space Dimensional Banach Space Disjoint Sequence Open Mapping Theorem Rigidity Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer 2001

Authors and Affiliations

  • Ion Chiţescu
    • 1
  1. 1.Faculty of MathematicsUniversity of BucharestBucharestRomania

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