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


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.


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Brézis H.,Analyse fonctionelle, Théorie et applications, Masson Paris, (1983).zbMATHGoogle Scholar
  2. [2]
    Chiţescu I.,Finitely Purely Atomic Measures and L p-Spaces, Analele Univ. Bucureşti ser. Şt. Naturii,24 (1975), 23–29.Google Scholar
  3. [3]
    Criţescu R.,Ordered Vector Spaces, Abacus Press Kent, (1976).Google Scholar
  4. [4]
    Day M. M.,Normed Linear Spaces, Springer Verlag, (1962).Google Scholar
  5. [5]
    Diestel J.,Sequences and Series in Banach Spaces, Springer Verlag, (1984).Google Scholar
  6. [6]
    Diestel J., Uhl J. J. Jr.,Vector Measures, Mathematical Surveys 15 American Mathematical Society, Providence Rhode Island, (1977).zbMATHGoogle Scholar
  7. [7]
    Dinculeanu N.,Vector Measures, Pergamon Press, Oxford, (1964).Google Scholar
  8. [8]
    Dunford N., Schwartz J. T.,Linear Operators part 1, Interscience Publishers Inc. New York, (1967).Google Scholar
  9. [9]
    Halmos P. R.,Measure Theory, D. van Nostrand Company Inc. Princeton, (1966).Google Scholar
  10. [10]
    Köthe G.,Topological Vector Spaces, vol. I, vol. II, Springer Verlag (1969). (1979).Google Scholar
  11. [11]
    Kufner A., John O., Fucik S.,Function Spaces, Akademia Publishing House of the Czechoslovak Academy of Sciences Prague, (1977).zbMATHGoogle Scholar
  12. [12]
    Meyer-Nieberg P.,Banach Lattices, Springer Verlag, (1991).Google Scholar
  13. [13]
    Schaefer H. H.,Topological Vector Spaces, Springer Verlag, (1970).Google Scholar

Copyright information

© Springer 2001

Authors and Affiliations

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

Personalised recommendations