On weakly uniformly rotund spaces
On weighted James' spaces.
In this note we study the topological structure of weighted James spaces J(h). In particular we prove that J(h) is isomorphic to J if and only if the weight h is bounded. We also provide a description of J(h) if the weight is a non-decreasing sequence.
On ω*-basic sequences and their applications to the study of Banach spaces
Order continuous linear functionals on non-locally convex Orlicz spaces
The space of all order continuous linear functionals on an Orlicz space defined by an arbitrary (not necessarily convex) Orlicz function is described.
Orthogonal bases in 1∞ (X).
Parties admissibles d'un espace de Banach. Applications
Pelczynski’s property for Banach spaces
Poisson's equation and characterizations of reflexivity of Banach spaces
Let X be a Banach space with a basis. We prove that X is reflexive if and only if every power-bounded linear operator T satisfies Browder’s equality = (I-T)XWe then deduce that X (with a basis) is reflexive if and only if every strongly continuous bounded semigroup with generator A satisfies . The range (I-T)X (respectively, AX for continuous time) is the space of x ∈ X for which Poisson’s equation (I-T)y = x (Ay = x in continuous time) has a solution y ∈ X; the above equalities for the ranges...
Preduals of Sobolev-Campanato spaces
We present definitions of Banach spaces predual to Campanato spaces and Sobolev-Campanato spaces, respectively, and we announce some results on embeddings and isomorphisms between these spaces. Detailed proofs will appear in our paper in Math. Nachr.
Préduaux d'espaces de Banach
Product spaces generated by bilinear maps and duality
In this paper we analyse a definition of a product of Banach spaces that is naturally associated by duality with a space of operators that can be considered as a generalization of the notion of space of multiplication operators. This dual relation allows to understand several constructions coming from different fields of functional analysis that can be seen as instances of the abstract one when a particular product is considered. Some relevant examples and applications are shown, regarding pointwise...
Projections in dual weakly compactly generated Banach spaces
Properly semi-L-embedded complex spaces
We prove the existence of complex Banach spaces X such that every element F in the bidual X** of X has a unique best approximation π(F) in X, the equality ∥F∥ = ∥π (F)∥ + ∥F - π (F)∥ holds for all F in X**, but the mapping π is not linear.
Properties and applications of Tauberian operators.
Tauberian operators, which appeared in response to a problem in summability [GaW, KW] have found application in several situations: factorization of operators [DFJP], preservation of isomorphic properties of Banach spaces [N, NR], equivalence between the Radon-Nikodym property and the Krein-Milman property [Sch], and generalized Fredholm operators [Ta, Y].This paper is a survey of the main properties and applications of Tauberian operators.
Propriété de Banach-Saks et modèles étalés
Propriétés de lissité de certaines normes. Applications a la dualité.
Propriétés locales et ultrapuissances d'espaces de Banach
Propriétés locales et ultrapuissances d'espaces de Banach (suite et fin)
Pták's characterization of reflexivity in tensor products
We characterize the reflexivity of the completed projective tensor products of Banach spaces in terms of certain approximative biorthogonal systems.
p-trivial Banach spaces