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Displaying 281 – 300 of 427

Radon-Nikodym property for vector-valued integrable functions

Surjit Singh Khurana (1978)

Annales de l'institut Fourier

It is proved that if a Frechet space $E$ has $R - N$ property, then $L_{p} (E, ν)$ also has $R - N$ property, for $1 < p < \infty$ .

Rank α operators on the space C(T,X)

Dumitru Popa (2002)

Colloquium Mathematicae

For 0 ≤ α < 1, an operator U ∈ L(X,Y) is called a rank α operator if $x ₙ \to^{τ_{α}} x$ 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.

José Bonet, Pawel Domanski (1998)

Monatshefte für Mathematik

Realcompactness and spaces of vector-valued functions

Jesus Araujo (2002)

Fundamenta Mathematicae

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.

JOCHEN WENGENROTH (1999)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

Regulated functions with values in Banach space

Dana Fraňková (2019)

Mathematica Bohemica

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

Giovanni Emmanuele (1996)

Commentationes Mathematicae Universitatis Carolinae

In the paper [5] L. Drewnowski and the author proved that if $X$ is a Banach space containing a copy of $c_{0}$ then $L_{1} (μ, X)$ is not complemented in $c a b v (μ, X)$ and conjectured that the same result is true if $X$ is any Banach space without the Radon-Nikodym property. Recently, F. Freniche and L. Rodriguez-Piazza ([7]) disproved this conjecture, by showing that if $μ$ is a finite measure and $X$ is a Banach lattice not containing copies of $c_{0}$ , then $L_{1} (μ, X)$ is complemented in $c a b v (μ, X)$ . Here, we show that the complementability of $L_{1} (μ, X)$ in $c a b v (μ, X)$ together...

Renorming in the Space of Bochner Intgrable Functions.

G. Schlüchtermann (1991)

Manuscripta mathematica

Representaciones de los espacios OM (E) y DLP (E).

José Bonet (1982)

Collectanea Mathematica

Representation of linear operators on spaces of vector valued functions

Romulus Cristescu (1984)

Mathematica Slovaca

Representation of multilinear operators on C(K, X) spaces.

Ignacio Villanueva (2002)

RACSAM

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.

Laurent Vanderputten (2001)

Extracta Mathematicae

Retractions and Open Mappings between Convex Sets.

Achim Clausing (1978)

Mathematische Zeitschrift

Riemann--Stieltjes operators between vector-valued weighted Bloch spaces.

Wang, Maofa (2008)

Journal of Inequalities and Applications [electronic only]

Rml;ume holomorpher Vektorfunktionen mit Wachstumsbedingungen und topologische Tensorprodukte.

Reinhold Meise (1972)

Mathematische Annalen

Schauder decompositions and multiplier theorems

P. Clément, B. de Pagter, F. Sukochev, H. Witvliet (2000)

Studia Mathematica

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 $L^{p}$ -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 $K$ -convexité

G. Pisier (1980/1981)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Semi-groupes holomorphes et $K$ -convexité (suite)

G. Pisier (1980/1981)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

Sharp embedding results for spaces of smooth functions with power weights

Martin Meyries, Mark Veraar (2012)

Studia Mathematica

We consider function spaces of Besov, Triebel-Lizorkin, Bessel-potential and Sobolev type on $ℝ^{d}$ , equipped with power weights $w (x) = {| x |}^{γ}$ , 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)

Marián Fabian, Sebastián Lajara (2012)

Studia Mathematica

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.

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