Dual spaces of JB*-triples and the Radon-Nikodym property.
Dual spaces to Orlicz-Lorentz spaces
For an Orlicz function φ and a decreasing weight w, two intrinsic exact descriptions are presented for the norm in the Köthe dual of the Orlicz-Lorentz function space or the sequence space , equipped with either the Luxemburg or Amemiya norms. The first description is via the modular , where f* is the decreasing rearrangement of f, ≺ denotes submajorization, and φ⁎ is the complementary function to φ. The second description is in terms of the modular ,where (f*)⁰ is Halperin’s level function...
Duality of Banach spaces
Duality of Lorentz Sequence Spaces d(w, p) (0<p<1).
Duality properties and Riesz representation theorem in Besicovitch-Musielak-Orlicz space of almost periodic functions
This paper is an extension of the work done in [Morsli M., Bedouhene F., Boulahia F., Duality properties and Riesz representation theorem in the Besicovitch-Orlicz space of almost periodic functions, Comment. Math. Univ. Carolin. 43 (2002), no. 1, 103--117] to the Besicovitch-Musielak-Orlicz space of almost periodic functions. Necessary and sufficient conditions for the reflexivity of this space are given. A Riesz type ``duality representation theorem'' is also stated.
Duality properties and Riesz representation theorem in the Besicovitch-Orlicz space of almost periodic functions
In [6], the classical Riesz representation theorem is extended to the class of Besicovitch space of almost periodic functions a.p., . It is also shown that this space is reflexive. We shall consider here such results in the context of Orlicz spaces, namely in the class of Besicovitch-Orlicz space of almost periodic functions a.p., where is an Orlicz function.
Duality, reflexivity and atomic decompositions in Banach spaces
We study atomic decompositions and their relationship with duality and reflexivity of Banach spaces. To this end, we extend the concepts of "shrinking" and "boundedly complete" Schauder basis to the atomic decomposition framework. This allows us to answer a basic duality question: when an atomic decomposition for a Banach space generates, by duality, an atomic decomposition for its dual space. We also characterize the reflexivity of a Banach space in terms of properties of its atomic decompositions....
Duaux transfinis.
Dunford-Pettis-like properties of continuous vector function spaces.
Dunford-Pettis-like properties of projective and natural tensor product spaces.
Several properties of weakly p-summable sequences and of the scale of p-converging operators (i.e., operators transforming weakly p-summable sequences into convergent sequences) in projective and natural tensor products with an lp space are considered. The last section studies the Dunford-Pettis property of order p (i.e., every weakly compact operator is p-convergent) in those spaces.
Dvoretzky Theorem - Thirty Years Later (Survey).