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On the class of positive almost weak Dunford-Pettis operators

Abderrahman Retbi (2015)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we introduce and study the class of almost weak Dunford-Pettis operators. As consequences, we derive the following interesting results: the domination property of this class of operators and characterizations of the wDP property. Next, we characterize pairs of Banach lattices for which each positive almost weak Dunford-Pettis operator is almost Dunford-Pettis.

On the class of positive disjoint weak p -convergent operators

Abderrahman Retbi (2024)

Mathematica Bohemica

We introduce and study the disjoint weak p -convergent operators in Banach lattices, and we give a characterization of it in terms of sequences in the positive cones. As an application, we derive the domination and the duality properties of the class of positive disjoint weak p -convergent operators. Next, we examine the relationship between disjoint weak p -convergent operators and disjoint p -convergent operators. Finally, we characterize order bounded disjoint weak p -convergent operators in terms...

On the derived tensor product functors for (DF)- and Fréchet spaces

Oğuz Varol (2007)

Studia Mathematica

For a (DF)-space E and a tensor norm α we investigate the derivatives T o r α l ( E , · ) of the tensor product functor E ̃ α · : from the category of Fréchet spaces to the category of linear spaces. Necessary and sufficient conditions for the vanishing of T o r ¹ α ( E , F ) , which is strongly related to the exactness of tensored sequences, are presented and characterizations in the nuclear and (co-)echelon cases are given.

On the diametral dimension of weighted spaces of analytic germs

Michael Langenbruch (2016)

Studia Mathematica

We prove precise estimates for the diametral dimension of certain weighted spaces of germs of holomorphic functions defined on strips near ℝ. This implies a full isomorphic classification for these spaces including the Gelfand-Shilov spaces S ¹ α and S α for α > 0. Moreover we show that the classical spaces of Fourier hyperfunctions and of modified Fourier hyperfunctions are not isomorphic.

On the Dirichlet problem for functions of the first Baire class

Jiří Spurný (2001)

Commentationes Mathematicae Universitatis Carolinae

Let be a simplicial function space on a metric compact space X . Then the Choquet boundary Ch X of is an F σ -set if and only if given any bounded Baire-one function f on Ch X there is an -affine bounded Baire-one function h on X such that h = f on Ch X . This theorem yields an answer to a problem of F. Jellett from [8] in the case of a metrizable set X .

On the distributive radical of an Archimedean lattice-ordered group

Ján Jakubík (2009)

Czechoslovak Mathematical Journal

Let G be an Archimedean -group. We denote by G d and R D ( G ) the divisible hull of G and the distributive radical of G , respectively. In the present note we prove the relation ( R D ( G ) ) d = R D ( G d ) . As an application, we show that if G is Archimedean, then it is completely distributive if and only if it can be regularly embedded into a completely distributive vector lattice.

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