Banach Lattices with Locally Compact Representation Spaces.
Banach space properties of strongly tight uniform algebras
We use the work of J. Bourgain to show that some uniform algebras of analytic functions have certain Banach space properties. If X is a Banach space, we say X is strongif X and X* have the Dunford-Pettis property, X has the Pełczyński property, and X* is weakly sequentially complete. Bourgain has shown that the ball-algebras and the polydisk-algebras are strong Banach spaces. Using Bourgain’s methods, Cima and Timoney have shown that if K is a compact planar set and A is R(K) or A(K), then A and...
Banach spaces
Banach spaces in which all multilinear forms are weakly sequentially continuous
We solve several problems in the theory of polynomials in Banach spaces. (i) There exist Banach spaces without the Dunford-Pettis property and without upper p-estimates in which all multilinear forms are weakly sequentially continuous: some Lorentz sequence spaces, their natural preduals and, most notably, the dual of Schreier's space. (ii) There exist Banach spaces X without the Dunford-Pettis property such that all multilinear forms on X and X* are weakly sequentially continuous; this gives an...
Banach spaces of functions analytic in a polydisc.
Banach Spaces of Locally Schlicht Functions with the Hornich Operations.
Banach Spaces of Solutions of the Hemholtz Equation in the Plane.
Banach Spaces Related to Integrable Group Representations and Their Atomic Decompositions. Part II.
Banach-Saks property in some Banach sequence spaces
It is proved that for any Banach space X property (β) defined by Rolewicz in [22] implies that both X and X* have the Banach-Saks property. Moreover, in Musielak-Orlicz sequence spaces, criteria for the Banach-Saks property, the near uniform convexity, the uniform Kadec-Klee property and property (H) are given.
Banach-Stone Theorems and Separating Maps.
Banach-Stone theorems for non-separably valued Bochner – spaces
Barrelled spaces with Boolean rings of projections.
The talk presented a survey of results most of which have been obtained over the last several years in collaboration with M.Florencio and P.J.Paúl (Seville). The results concern the question of barrelledness of locally convex spaces equipped with suitable Boolean algebras or rings of projections. They are particularly applicable to various spaces of measurable vector valued functions. Some of the results are provided with proofs that are much simpler than the original ones.
Barrelledness Conditions on S (...;E) and B(...;E).
Barrelledness of generalized sums of normed spaces
Let be a family of normed spaces and a space of scalar generalized sequences. The -sum of the family of spaces is Starting from the topology on and the norm topology on each a natural topology on can be defined. We give conditions for to be quasi-barrelled, barrelled or locally complete.
Barrelledness of the Space of Vector Valued and Simple Functions.
Bases de Schauder dans certains espaces de fonctions holomorphes
On étudie les bases de Schauder pour fonctions holomorphes et leurs applications à l’approximation et interpolation.Après avoir établi quelques faits généraux sur les bases et semi-bases, on les applique à l’étude des bases formées par une suite simple de polynômes.L’effort principal est porté sur la preuve de l’existence d’une “bonne” base commune des espaces des fonctions holomorphes sur et , où est un domaine de et un compact dans tels que soit un domaine régulier pour le problème...
Bases from orthogonal subspaces obtained by evaluation of the reproducing kernel.
Bases in spaces of analytic germs
We prove precise decomposition results and logarithmically convex estimates in certain weighted spaces of holomorphic germs near ℝ. These imply that the spaces have a basis and are tamely isomorphic to the dual of a power series space of finite type which can be calculated in many situations. Our results apply to the Gelfand-Shilov spaces and for α > 0 and to the spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions.
Bases in the space analytic Dirichlet transformations.
Bases in the spaces and