On duals of Calderón-Lozanovskiĭ intermediate spaces

Yves Raynaud

Studia Mathematica (1997)

  • Volume: 124, Issue: 1, page 9-36
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Raynaud, Yves. "On duals of Calderón-Lozanovskiĭ intermediate spaces." Studia Mathematica 124.1 (1997): 9-36. <http://eudml.org/doc/216399>.

@article{Raynaud1997,
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.},
author = {Raynaud, Yves},
journal = {Studia Mathematica},
keywords = {Calderón-Lozanovskiĭ intermediate space; Banach Köthe function spaces},
language = {eng},
number = {1},
pages = {9-36},
title = {On duals of Calderón-Lozanovskiĭ intermediate spaces},
url = {http://eudml.org/doc/216399},
volume = {124},
year = {1997},
}

TY - JOUR
AU - Raynaud, Yves
TI - On duals of Calderón-Lozanovskiĭ intermediate spaces
JO - Studia Mathematica
PY - 1997
VL - 124
IS - 1
SP - 9
EP - 36
AB - 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.
LA - eng
KW - Calderón-Lozanovskiĭ intermediate space; Banach Köthe function spaces
UR - http://eudml.org/doc/216399
ER -

References

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  1. [A] T. Andô, Linear functionals on Orlicz spaces, Nieuw Arch. Wisk. 8 (1960), 1-16. Zbl0129.08001
  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. Zbl0204.13703
  4. [F] R. Fernandez, Characterization of the dual of an Orlicz space, Comment. Math. 30 (1990), 69-83. Zbl0753.46023
  5. [Fr] D. H. Fremlin, Topological Riesz Spaces and Measure Theory, Cambridge University Press, 1974. Zbl0273.46035
  6. [K] K. D. Kürsten, Lokale Reflexivität und lokale Dualität von Ultraprodukten für halbgeordnete Banachräume, Z. Anal. Anwendungen 3 (1984), 245-262. Zbl0544.46007
  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. Zbl0403.46022
  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. 

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