Convolutions and products of partially ordered vector-valued positive measures.
Copies of in the space of Pettis integrable functions with integrals of finite variation
Let (Ω,Σ,μ) be a complete finite measure space and X a Banach space. We show that the space of all weakly μ-measurable (classes of scalarly equivalent) X-valued Pettis integrable functions with integrals of finite variation, equipped with the variation norm, contains a copy of if and only if X does.
Copies of lp in tensor products.
The problem of finding complemented copies of lp in another space is a classical problem in Functional Analysis and has been studied from different points of view in the literature. Here we pay attention to complementation of lp in an n-fold tensor product of lq spaces because we were lead to that result in the study of Grothendieck's Problème des topologies as we shall comment later.
Correction to "On Malgrange Theorem for Nuclear Holomorphic Functions in Open Balls of a Banach Space".
Correction to the paper ’Copies of in the space of Pettis integrable functions with integrals of finite variation’ (Studia Math. 210 (2012), 93-98)
Correction to “Unconditionally converging and Dunford-Pettis operators on ” ( Studia Math. 57 (1976), pp. 85-90)
Corrigenda to "Differentiable mappings on topological vector spaces" (Studia Math 45(1972),pp. 147-160)
Cotype and absolutely summing homogeneous polynomials in spaces
We lift to homogeneous polynomials and multilinear mappings a linear result due to Lindenstrauss and Pełczyński for absolutely summing operators. We explore the notion of cotype to obtain stronger results and provide various examples of situations in which the space of absolutely summing homogeneous polynomials is different from the whole space of homogeneous polynomials. Among other consequences, these results enable us to obtain answers to some open questions about absolutely summing homogeneous...
Countable sets of holomorphic mappings
Counterexamples in Holomorphic Functions on Nuclear Fréchet Spaces.
Criteria for weak compactness of vector-valued integration maps
Criteria are given for determining the weak compactness, or otherwise, of the integration map associated with a vector measure. For instance, the space of integrable functions of a weakly compact integration map is necessarily normable for the mean convergence topology. Results are presented which relate weak compactness of the integration map with the property of being a bicontinuous isomorphism onto its range. Finally, a detailed description is given of the compactness properties for the integration...
Décomposition et classification des systèmes dynamiques
Delta-convex mappings between Banach spaces and applications [Book]
Denjoy integral and Henstock-Kurzweil integral in vector lattices. II
In a previous paper we defined a Denjoy integral for mappings from a vector lattice to a complete vector lattice. In this paper we define a Henstock-Kurzweil integral for mappings from a vector lattice to a complete vector lattice and consider the relation between these two integrals.
Denjoy integral and Henstock-Kurzweil integral in vector lattices. I
In this paper we define the derivative and the Denjoy integral of mappings from a vector lattice to a complete vector lattice and show the fundamental theorem of calculus.
Denseness and Borel complexity of some sets of vector measures
Let ν be a positive measure on a σ-algebra Σ of subsets of some set and let X be a Banach space. Denote by ca(Σ,X) the Banach space of X-valued measures on Σ, equipped with the uniform norm, and by ca(Σ,ν,X) its closed subspace consisting of those measures which vanish at every ν-null set. We are concerned with the subsets and of ca(Σ,X) defined by the conditions |φ| = ν and |φ| ≥ ν, respectively, where |φ| stands for the variation of φ ∈ ca(Σ,X). We establish necessary and sufficient conditions...
Denseness of numerical radius attaining holomorphic functions.
Dentabilité et points extrémaux
Derivability, variation and range of a vector measure
We prove that the range of a vector measure determines the σ-finiteness of its variation and the derivability of the measure. Let F and G be two countably additive measures with values in a Banach space such that the closed convex hull of the range of F is a translate of the closed convex hull of the range of G; then F has a σ-finite variation if and only if G does, and F has a Bochner derivative with respect to its variation if and only if G does. This complements a result of [Ro] where we proved...
Derivación de medidas e integración vectorial bilineal.