Download PDF - On duals of Calderón-Lozanovskiĭ intermediate spacesAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

On duals of Calderón-Lozanovskiĭ intermediate spaces

Authors 1

Affiliations

  1. Equipe d'Analyse (CNRS), Université Paris 6, 4, place Jussieu, 75252 Paris Cedex 05, France

Abstract

We give a description of the dual of a Calderón-Lozanovskiĭ intermediate space φ(X,Y) of a couple of Banach Köthe function spaces as an intermediate space ψ(X*,Y*) of the duals, associated with a "variable" function ψ.

Bibliography

  1. [A] T. Andô, Linear functionals on Orlicz spaces, Nieuw Arch. Wisk. 8 (1960), 1-16.
  2. [Au] R. J. Aumann, Measurable utility and the measurable choice theorem, in: Proc. Conf. La Décision 2, Aix-en-Provence 1967, Actes Colloq. Internat. CNRS 171, CNRS, 1969, 15-26.
  3. [C] A. P. Calderón, Intermediate spaces and interpolation, the complex method, Studia Math. 24 (1964), 113-190.
  4. [F] R. Fernandez, Characterization of the dual of an Orlicz space, Comment. Math. 30 (1990), 69-83.
  5. [Fr] D. H. Fremlin, Topological Riesz Spaces and Measure Theory, Cambridge University Press, 1974.
  6. [K] K. D. Kürsten, Lokale Reflexivität und lokale Dualität von Ultraprodukten für halbgeordnete Banachräume, Z. Anal. Anwendungen 3 (1984), 245-262.
  7. [L1] G. Ya. Lozanovskiĭ, On some Banach lattices, Siberian Math. J. 10 (1969), 419-431 (English transl.).
  8. [L2] G. Ya. Lozanovskiĭ, On some Banach lattices III, ibid. 13 (1972), 910-916 (English transl.).
  9. [L3] G. Ya. Lozanovskiĭ, On some Banach lattices IV, ibid. 14 (1973) 97-108 (English transl.).
  10. [LT] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II: Function Spaces, Ergeb. Math. Grenzgeb. 97, Springer, 1979.
  11. [R] S. Reisner, On two theorems of Lozanovskiĭ concerning intermediate Banach lattices, in: Geometric Aspects of Functional Analysis (Israel GAFA Seminar, 1986-87), Lecture Notes in Math. 1317, Springer, 1988, 67-83.
  12. [VL] B. Z. Vulikh and G. Ya. Lozanovskiĭ, On the representation of completely linear and regular functionals in partially ordered spaces, Math. USSR-Sb. 13 (1971), 323-343 (English transl.).
  13. [Z] A. C. Zaanen, Integration, North-Holland, 1967.
Studia Mathematica
1997/124/1
Export to PBN, Opens in new tab
Pages:
9-36
Main language of publication
English
Received
1996-01-02
Accepted
1996-10-28
Published
1997
Exact and natural sciences