Construction of an orthonormal basis in and
Containing l1 or c0 and best approximation.
The purpose of this paper is to obtain sufficient conditions, for a Banach space X to contain or exclude c0 or l1, in terms of the sets of best approximants in X for the elements in the bidual space.
Continuity of operators on Saks spaces
Continuity of superposition operators on and
Continuity of the uniform rotundity modulus relative to linear subspaces
We prove the continuity of the rotundity modulus relative to linear subspaces of normed spaces. As a consequence we reduce the study of uniform rotundity relative to linear subspaces to the study of the same property relative to closed linear subspaces of Banach spaces.
Continuity properties of projection operators.
Continuity properties up to a countable partition.
Approximation and rigidity properties in renorming constructions are characterized with some classes of simple maps. Those maps describe continuity properties up to a countable partition. The construction of such kind of maps can be done with ideas from the First Lebesgue Theorem. We present new results on the relationship between Kadec and locally uniformly rotund renormability as well as characterizations of the last one with the simple maps used here.
Continuous and generalized solutions of singular partial differential equations.
Continuous mappings of a Banach space into a space
Continuous multilinear operators on C(K) spaces and polymeasures.
Continuous Position and Existence Sets.
Continuous restrictions of linear functionals
Continuous version of the Choquet integral representation theorem
Let E be a locally convex topological Hausdorff space, K a nonempty compact convex subset of E, μ a regular Borel probability measure on E and γ > 0. We say that the measure μ γ-represents a point x ∈ K if for any f ∈ E*. In this paper a continuous version of the Choquet theorem is proved, namely, if P is a continuous multivalued mapping from a metric space T into the space of nonempty, bounded convex subsets of a Banach space X, then there exists a weak* continuous family of regular Borel...
Contractive projections in Orlicz sequence spaces.
Contre-exemple à la propriété d'approximation uniforme dans les espaces de Banach
Convergence des martingales pluri-sous-harmoniques vectorielles à deux indices
Convergence of convex functions and generalized inf-convolutive approximations. (Convergences des fonctions convexes et approximations inf-convolutives généralisées.)
Convergence of greedy approximation I. General systems
We consider convergence of thresholding type approximations with regard to general complete minimal systems eₙ in a quasi-Banach space X. Thresholding approximations are defined as follows. Let eₙ* ⊂ X* be the conjugate (dual) system to eₙ; then define for ε > 0 and x ∈ X the thresholding approximations as , where . We study a generalized version of that we call the weak thresholding approximation. We modify the in the following way. For ε > 0, t ∈ (0,1) we set and consider the weak...
Convergence of series and isomorphic embeddings in Banach spaces
Convergence of Taylor series in Hardy and Besov spaces.