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Almost demi Dunford--Pettis operators on Banach lattices

Hedi Benkhaled (2023)

Commentationes Mathematicae Universitatis Carolinae

We introduce new concept of almost demi Dunford–Pettis operators. Let E be a Banach lattice. An operator T from E into E is said to be almost demi Dunford–Pettis if, for every sequence { x n } in E + such that x n 0 in σ ( E , E ' ) and x n - T x n 0 as n , we have x n 0 as n . In addition, we study some properties of this class of operators and its relationships with others known operators.

AM-Compactness of some classes of operators

Belmesnaoui Aqzzouz, Jawad H'michane (2012)

Commentationes Mathematicae Universitatis Carolinae

We characterize Banach lattices on which each regular order weakly compact (resp. b-weakly compact, almost Dunford-Pettis, Dunford-Pettis) operator is AM-compact.

An elementary proof of a theorem on sublattices of finite codimension

Marek Wójtowicz (1998)

Commentationes Mathematicae Universitatis Carolinae

This paper presents an elementary proof and a generalization of a theorem due to Abramovich and Lipecki, concerning the nonexistence of closed linear sublattices of finite codimension in nonatomic locally solid linear lattices with the Lebesgue property.

Caractérisation des espaces vectoriels ordonnés sous-jacents aux algèbres de von Neumann

Alain Connes (1974)

Annales de l'institut Fourier

Nous démontrons que la catégorie de von Neumann est équivalente à la catégorie des cônes autopolaires, facialement homogènes, complexes. Un cône dans un espace hilbertien réel est dit : 1) facialement homogène quand pour toute face F de l’opérateur δ = (Projection sur F - F ) - (Projection sur F - F ) est une dérivation de (i.e. e t δ = t R ) ; 2) complexe quand on s’est donné une structure d’algèbre de Lie complexe sur l’algèbre de Lie réelle des dérivations de , modulo son centre. Nous caractérisons les espaces...

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