Renorming dual Banach lattices

Ghoussoub, N.

doi:10.1090/S0002-9939-1982-0643741-2

Renorming dual Banach lattices
HTML articles powered by AMS MathViewer

by N. Ghoussoub PDF

Proc. Amer. Math. Soc. 84 (1982), 521-524 Request permission

Abstract:

We show that a Banach lattice is order continuous as well as its dual if and only if it admits an equivalent Fréchet differentiable and locally uniformly convex lattice norm such that its dual norm is also locally uniformly convex.

References

William J. Davis, Nassif Ghoussoub, and Joram Lindenstrauss, A lattice renorming theorem and applications to vector-valued processes, Trans. Amer. Math. Soc. 263 (1981), no. 2, 531–540. MR 594424, DOI 10.1090/S0002-9947-1981-0594424-2
Joseph Diestel, Geometry of Banach spaces—selected topics, Lecture Notes in Mathematics, Vol. 485, Springer-Verlag, Berlin-New York, 1975. MR 0461094

The long James space

Ivar Ekeland and Gérard Lebourg, Generic Fréchet-differentiability and perturbed optimization problems in Banach spaces, Trans. Amer. Math. Soc. 224 (1976), no. 2, 193–216 (1977). MR 431253, DOI 10.1090/S0002-9947-1976-0431253-2
Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. II, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 97, Springer-Verlag, Berlin-New York, 1979. Function spaces. MR 540367

The Radon-Nikodym property in Banach lattices

Banach lattices and positive operators

L. Vašák, On one generalization of weakly compactly generated Banach spaces, Studia Math. 70 (1981), no. 1, 11–19. MR 646957, DOI 10.4064/sm-70-1-11-19
Michel Talagrand, Dual Banach lattices and Banach lattices with the Radon-Nikodým property, Israel J. Math. 38 (1981), no. 1-2, 46–50. MR 599474, DOI 10.1007/BF02761847