Radon-Nikodym property for vector-valued integrable functions
It is proved that if a Frechet space has property, then also has property, for .
Rank α operators on the space C(T,X)
For 0 ≤ α < 1, an operator U ∈ L(X,Y) is called a rank α operator if implies Uxₙ → Ux in norm. We give some results on rank α operators, including an interpolation result and a characterization of rank α operators U: C(T,X) → Y in terms of their representing measures.
Real Analytic Curves in Fréchet Spaces and Their Duals.
Realcompactness and spaces of vector-valued functions
It is shown that the existence of a biseparating map between a large class of spaces of vector-valued continuous functions A(X,E) and A(Y,F) implies that some compactifications of X and Y are homeomorphic. In some cases, conditions are given to warrant the existence of a homeomorphism between the realcompactifications of X and Y; in particular we find remarkable differences with respect to the scalar context: namely, if E and F are infinite-dimensional and T: C*(X,E) → C*(Y,F) is a biseparating...
Regularity of general weighted inductive limits.
Regulated functions with values in Banach space
This paper deals with regulated functions having values in a Banach space. In particular, families of equiregulated functions are considered and criteria for relative compactness in the space of regulated functions are given.
Remarks on the complementability of spaces of Bochner integrable functions in spaces of vector measures
In the paper [5] L. Drewnowski and the author proved that if is a Banach space containing a copy of then is not complemented in and conjectured that the same result is true if is any Banach space without the Radon-Nikodym property. Recently, F. Freniche and L. Rodriguez-Piazza ([7]) disproved this conjecture, by showing that if is a finite measure and is a Banach lattice not containing copies of , then is complemented in . Here, we show that the complementability of in together...
Renorming in the Space of Bochner Intgrable Functions.
Representaciones de los espacios OM (E) y DLP (E).
Representation of linear operators on spaces of vector valued functions
Representation of multilinear operators on C(K, X) spaces.
We present a Riesz type representation theorem for multilinear operators defined on the product of C(K,X) spaces with values in a Banach space. In order to do this we make a brief exposition of the theory of operator valued polymeasures.
Representation of operators defined on the space of Bochner integrable functions.
Retractions and Open Mappings between Convex Sets.
Riemann--Stieltjes operators between vector-valued weighted Bloch spaces.
Rml;ume holomorpher Vektorfunktionen mit Wachstumsbedingungen und topologische Tensorprodukte.
Schauder decompositions and multiplier theorems
We study the interplay between unconditional decompositions and the R-boundedness of collections of operators. In particular, we get several multiplier results of Marcinkiewicz type for -spaces of functions with values in a Banach space X. Furthermore, we show connections between the above-mentioned properties and geometric properties of the Banach space X.
Semi-groupes holomorphes et -convexité
Semi-groupes holomorphes et -convexité (suite)
Sharp embedding results for spaces of smooth functions with power weights
We consider function spaces of Besov, Triebel-Lizorkin, Bessel-potential and Sobolev type on , equipped with power weights , γ > -d. We prove two-weight Sobolev embeddings for these spaces. Moreover, we precisely characterize for which parameters the embeddings hold. The proofs are presented in such a way that they also hold for vector-valued functions.
Smooth renormings of the Lebesgue-Bochner function space L¹(μ,X)
We show that, if μ is a probability measure and X is a Banach space, then the space L¹(μ,X) of Bochner integrable functions admits an equivalent Gâteaux (or uniformly Gâteaux) smooth norm provided that X has such a norm, and that if X admits an equivalent Fréchet (resp. uniformly Fréchet) smooth norm, then L¹(μ,X) has an equivalent renorming whose restriction to every reflexive subspace is Fréchet (resp. uniformly Fréchet) smooth.