Representation of operators by bilinear integrals
Representation of operators with martingales and the Radon-Nikodým property.
The Radon-Nikodým property was introduced to describe those Banach spaces X for which all operators acting between L1 and X have a representation function. These spaces can be characterized in terms of martingales, as those spaces in which every uniformly bounded martingale converges. In the present work we study some classes of operators defined upon their behaviour with respect to the convergence of such martingales. We prove that an operator preserves the non-convergence of uniformly bounded...
Representation of vector measures.
Representations of generalized measures by integrals
Resultados Recientes Sobre Espacios Polinomiales De Tipo Numerable.
Résultats récents sur les formes positives sur des espaces de fonctions
Reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces.
Riemann type integrals for functions taking values in a locally convex space
The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.
Riesz spaces valued measures and processes
Rigidity of holomorphic isometries
A rigidity theorem for holomorphic families of holomorphic isometries acting on Cartan domains is proved.
Rigidity of holomorphic maps and distortion of biholomorphic maps in operator Siegel domains
Results concerning the rigidity of holomorphic maps and the distortion of biholomorphic maps in infinite dimensional Siegel domains of -algebras are established. The homogeneity of the open unit balls in these algebras plays a key role in the arguments.
Rings of PDE-preserving operators on nuclearly entire functions
Let E,F be Banach spaces where F = E’ or vice versa. If F has the approximation property, then the space of nuclearly entire functions of bounded type, , and the space of exponential type functions, Exp(F), form a dual pair. The set of convolution operators on (i.e. the continuous operators that commute with all translations) is formed by the transposes , φ ∈ Exp(F), of the multiplication operators φ :ψ ↦ φ ψ on Exp(F). A continuous operator T on is PDE-preserving for a set ℙ ⊆ Exp(F) if it...
Rolle's theorem and negligibility of points in infinite dimensional Banach spaces.
Rotation-invariant operators on white noise functional.
Schauder bases and the bounded approximation property in separable Banach spaces
Let E be a separable Banach space with the λ-bounded approximation property. We show that for each ϵ > 0 there is a Banach space F with a Schauder basis such that E is isometrically isomorphic to a 1-complemented subspace of F and, moreover, the sequence (Tₙ) of canonical projections in F has the properties and . This is a sharp quantitative version of a classical result obtained independently by Pełczyński and by Johnson, Rosenthal and Zippin.
Schauder Type Theorems for Differentiable and Holomorphic Mappings.
Schur class operator functions and automorphisms of Hardy algebras.
Second order differentiability and Lipschitz smooth points of convex functionals
Second order differentiability of integral functionals on Sobolev spaces and L2-spaces.
Sections in function spaces