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A bounded linear operator between Banach spaces is called a Dieudonné operator ( = weakly completely continuous operator) if it maps weakly Cauchy sequences to weakly convergent sequences. Let (Ω,Σ,μ) be a finite measure space, and let X and Y be Banach spaces. We study Dieudonné operators T: L¹(X) → Y. Let $i_{\infty} : L^{\infty} (X) \to L ¹ (X)$ stand for the canonical injection. We show that if X is almost reflexive and T: L¹(X) → Y is a Dieudonné operator, then $T \circ i_{\infty} : L^{\infty} (X) \to Y$ is a weakly compact operator. Moreover, we obtain that if T: L¹(X)...

Dieudonné property

Surjit Singh Khurana (2002)

Mathematica Slovaca

Dieudonné-type theorems for lattice group-valued $k$ -triangular set functions

Antonio Boccuto, Xenofon Dimitriou (2019)

Kybernetika

Some versions of Dieudonné-type convergence and uniform boundedness theorems are proved, for $k$ -triangular and regular lattice group-valued set functions. We use sliding hump techniques and direct methods. We extend earlier results, proved in the real case. Furthermore, we pose some open problems.

Diffeomorphisms between spheres and hyperplanes in infinite-dimensional Banach spaces

Daniel Azagra (1997)

Studia Mathematica

Diffeotopy functors of ind-algebras and local cyclic cohomology.

Puschnigg, Michael (2003)

Documenta Mathematica

Difference Equations over p-adic Fields.

M. van der Put (1972)

Mathematische Annalen

Difference sequence spaces.

Gaur, A.K., Mursaleen (1998)

International Journal of Mathematics and Mathematical Sciences

Differences of weighted composition operators on $H_{α}^{\infty} {(B_{N})}^{*}$ .

Dai, Jineng, Ouyang, Caiheng (2009)

Journal of Inequalities and Applications [electronic only]

Different aspects of differentiability [Book]

(1995)

Differentation under the integral sign and holomorphy.

Sten Bjon (1987)

Mathematica Scandinavica

Differentiability from the representation formula and the Sobolev-Poincaré inequality

Valentino Magnani (2005)

Studia Mathematica

In the geometries of stratified groups, we provide differentiability theorems for both functions of bounded variation and Sobolev functions. Proofs are based on a systematic application of the Sobolev-Poincaré inequality and the so-called representation formula.

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