(Annexe n° 2) Un exemple concernant la super-réflexivité
Application à la Dualité d'une Propriété d'Intersection de Boules.
Application of Duality Theory to spaces of Measures
Approximationszahlen, p-nukleare Operatoren und Hilbertraumcharakterisierungen.
Arbres dont toutes les branches sont faiblement Cauchy
Banach spaces all of whose subspaces have the approximation property
Banach spaces and operators which are nearly uniformly convex [Book]
Banach spaces not having copies of 1 ∞ and Z1.
Banach spaces of bounded Szlenk index
For a countable ordinal α we denote by the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by α. We show that each admits a separable, reflexive universal space. We also show that spaces in the class embed into spaces of the same class with a basis. As a consequence we deduce that each is analytic in the Effros-Borel structure of subspaces of C[0,1].
Banach Spaces of Compact Multipliers and Their Dual Spaces.
Banach spaces on which every unconditionally converging operator is completely continuous
Banach spaces quasi-reflexive of order one
Banach spaces which are -ideals in their bidual have property
We show that every Banach space which is an -ideal in its bidual has the property of Pelczynski. Several consequences are mentioned.
Banachian Differentiable Spaces.
Bases and Quasi-reflexivity of Banach Spaces.
Bases y casirreflexividad en espacios de Banach.
Bidual Spaces and Reflexivity of Real Normed Spaces
In this article, we considered bidual spaces and reflexivity of real normed spaces. At first we proved some corollaries applying Hahn-Banach theorem and showed related theorems. In the second section, we proved the norm of dual spaces and defined the natural mapping, from real normed spaces to bidual spaces. We also proved some properties of this mapping. Next, we defined real normed space of R, real number spaces as real normed spaces and proved related theorems. We can regard linear functionals...
Characterization of normed linear spaces with generalized Mazur intersection property
Let 𝓐 be a compatible collection of bounded subsets in a normed linear space. We give a characterization of the following generalized Mazur intersection property: every closed convex set A ∈ 𝓐 is an intersection of balls.
Characterizations of almost transitive superreflexive Banach spaces
Almost transitive superreflexive Banach spaces have been considered in [7] (see also [4] and [6]), where it is shown that such spaces are uniformly convex and uniformly smooth. We prove that convex transitive Banach spaces are either almost transitive and superreflexive (hence uniformly smooth) or extremely rough. The extreme roughness of a Banach space means that, for every element in the unit sphere of , we have We note that, in general, the property of convex transitivity for a Banach...
Characterizations of elements of a double dual Banach space and their canonical reproductions
For every element x** in the double dual of a separable Banach space X there exists the sequence of the canonical reproductions of x** in the even-order duals of X. In this paper we prove that every such sequence defines a spreading model for X. Using this result we characterize the elements of X**╲ X which belong to the class (resp. to the class ) as the elements with the sequence equivalent to the usual basis of (resp. as the elements with the sequence equivalent to the usual basis...