The completely continuous property in Orlicz spaces.
We show that in Orlicz spaces equipped with Luxemburg norm and Orlicz norm, the RNP, CCP, PCP and CPCP are equivalent.
The dual of every Asplund space admits a projectional resolution of the identity
The dual of the James tree space is asymptotically uniformly convex
The dual of the James tree space is asymptotically uniformly convex.
The Dunford-Pettis property in C*-algebras
The Point of Continuity Property: Descriptive Complexity and Ordinal Index
∗ Supported by D.G.I.C.Y.T. Project No. PB93-1142Let X be a separable Banach space without the Point of Continuity Property. When the set of closed subsets of its closed unit ball is equipped with the standard Effros-Borel structure, the set of those which have the Point of Continuity Property is non-Borel. We also prove that, for any separable Banach space X, the oscillation rank of the identity on X (an ordinal index which quantifies the Point of Continuity Property) is determined by the subspaces...
The problem of complementability for some spaces of vector measures of bounded variation with values in Banach spaces containing copies of
Let (S, ∑, m) be any atomless finite measure space, and X any Banach space containing a copy of . Then the Bochner space is uncomplemented in ccabv(∑,m;X), the Banach space of all m-continuous vector measures that are of bounded variation and have a relatively compact range; and ccabv(∑,m;X) is uncomplemented in cabv(∑,m;X). It is conjectured that this should generalize to all Banach spaces X without the Radon-Nikodym property.
The projective tensor product (II): the Radon-Nikodym property.
In this paper we discuss the problem of when the projective tensor product of two Banach spaces has the Radon-Nikodym property. We give a detailed exposition of the famous examples of Jean Bourgain and Gilles Pisier showing that there are Banach spaces X and Y such that each has the Radon-Nikodym property but for which their projective tensor product does not; this result depends on the classical theory of absolutely summing, integral and nuclear operators, as well as the famous Grothendieck inequality...
The Radon--Nikodym theorem for reflexive Banach spaces.
The stability of bases in Banach and Hilbert spaces.
The strong WCD property for Banach spaces.
The weak Phillips property
Let X be a Banach space. If the natural projection p:X*** → X* is sequentially weak*-weak continuous then the space X is said to have the weak Phillips property. We present several characterizations of the spaces having this property and study its relationships to other Banach space properties, especially the Grothendieck property.
The weak Radon-Nikodym property
The weak Radon-Nikodym property in Banach spaces
The -approximation property and the weak topology in tensor products of Banach spaces
Theorems of Krein Milman type for certain convex sets of functions operators
Sufficient conditions are given in order that, for a bounded closed convex subset of a locally convex space , the set of continuous functions from the compact space into , is the uniformly closed convex hull in of its extreme points. Applications are made to the unit ball of bounded (or compact, or weakly compact) operators from certain Banach spaces into .
Transitivity of the norm on Banach spaces.
Translations mesurables et ensembles de Rosenthal