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On the class of order Dunford-Pettis operators

Khalid Bouras, Abdelmonaim El Kaddouri, Jawad H'michane, Mohammed Moussa (2013)

Mathematica Bohemica

We characterize Banach lattices $E$ and $F$ on which the adjoint of each operator from $E$ into $F$ which is order Dunford-Pettis and weak Dunford-Pettis, is Dunford-Pettis. More precisely, we show that if $E$ and $F$ are two Banach lattices then each order Dunford-Pettis and weak Dunford-Pettis operator $T$ from $E$ into $F$ has an adjoint Dunford-Pettis operator $T^{'}$ from $F^{'}$ into $E^{'}$ if, and only if, the norm of $E^{'}$ is order continuous or $F^{'}$ has the Schur property. As a consequence we show that, if $E$ and $F$ are two Banach...

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 Cohen $p$ -nuclear sublinear operators.

Achour, Dahmane, Mezrag, Lahcène, Saadi, Khalil (2009)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

On the equality between some classes of operators on Banach lattices

Belmesnaoui Aqzzouz, Aziz Elbour, Mohammed Moussa (2012)

Mathematica Bohemica

We establish some sufficient conditions under which the subspaces of Dunford-Pettis operators, of M-weakly compact operators, of L-weakly compact operators, of weakly compact operators, of semi-compact operators and of compact operators coincide and we give some consequences.

On the positivity of the unit element in a normed lattice ordered algebra

S. Bernau, C. Huijsmans (1990)

Studia Mathematica

On the sublinear operators factoring through $L_{q}$ .

Mezrag, Lahcène, Tiaiba, Abdelmoumene (2004)

International Journal of Mathematics and Mathematical Sciences

On the upper envelopes of a family of $n$ -disjoint operators.

Radnaev, V.A. (2001)

Vladikavkazskiĭ Matematicheskiĭ Zhurnal

On W*UR point and UR point of Orlicz spaces with Orlicz norm.

Ting Fu Wang, Zhong Rui Shi, Quan Di Wang (1993)

Collectanea Mathematica

For Orlicz spaces with Orlicz norm, a criterion of W*UR point is given, and previous results about UR points and WUR points are amended.

Opérateurs sommants sur un cone normal d un espace de Banach.

Richard Becker (1993)

Collectanea Mathematica

The aim of this paper is to develop a theory of p-summing operators (between Banach spaces) in presence of an order structure given by a convex normal cone.

Order theory and interpolation in operator algebras

David P. Blecher, Charles John Read (2014)

Studia Mathematica

In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain C*-algebraic results and theories to more general algebras. Here we continue to develop this positivity and its associated ordering, proving many foundational facts. We also give many applications, for example to noncommutative topology, noncommutative peak sets, lifting problems, peak interpolation, approximate identities, and to order relations between an operator...

Orthogonally additive operators on lattice-normed spaces.

Kusraev, A.G., Pliev, M.A. (1999)

Vladikavkazskiĭ Matematicheskiĭ Zhurnal

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