Double-dual types over the Banach space .
DP1 and completely continuous operators.
Drop property equals reflexivity
Dual Banach algebras: representations and injectivity
We study representations of Banach algebras on reflexive Banach spaces. Algebras which admit such representations which are bounded below seem to be a good generalisation of Arens regular Banach algebras; this class includes dual Banach algebras as defined by Runde, but also all group algebras, and all discrete (weakly cancellative) semigroup algebras. Such algebras also behave in a similar way to C*- and W*-algebras; we show that interpolation space techniques can be used in place of GNS type arguments....
Dual properties for unconditionally converging operators
Dual renormings of Banach spaces
We prove that a Banach space admitting an equivalent WUR norm is an Asplund space. Some related dual renormings are also presented.
Dual results of factorization for operators.
Dual spaces generated by the interior of the set of norm attaining functionals
We characterize some isomorphic properties of Banach spaces in terms of the set of norm attaining functionals. The main result states that a Banach space is reflexive as soon as it does not contain ℓ₁ and the dual unit ball is the w*-closure of the convex hull of elements contained in the "uniform" interior of the set of norm attaining functionals. By assuming a very weak isometric condition (lack of roughness) instead of not containing ℓ₁, we also obtain a similar result. As a consequence of the...
Dual spaces of compact operator spaces and the weak Radon-Nikodým property
We deal with the weak Radon-Nikodým property in connection with the dual space of (X,Y), the space of compact operators from a Banach space X to a Banach space Y. First, under the weak Radon-Nikodým property, we give a representation of that dual. Next, using this representation, we provide some applications to the dual spaces of (X,Y) and , the space of weak*-weakly continuous operators.
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).