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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 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 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.

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...

Positive bases in ordered subspaces with the Riesz decomposition property

Vasilios Katsikis, Ioannis A. Polyrakis (2006)

Studia Mathematica

In this article we suppose that E is an ordered Banach space whose positive cone is defined by a countable family ℱ = f i | i ∈ ℕ of positive continuous linear functionals on E, i.e. E₊ = x ∈ E | f i ( x ) ≥ 0 for each i, and we study the existence of positive (Schauder) bases in ordered subspaces X of E with the Riesz decomposition property. We consider the elements x of E as sequences x = ( f i ( x ) ) and we develop a process of successive decompositions of a quasi-interior point of X₊ which at each step gives elements with smaller support....

Some characterizations of order weakly compact operator

Belmesnaoui Aqzzouz, Aziz Elbour (2011)

Mathematica Bohemica

We introduce the notion of order weakly sequentially continuous lattice operations of a Banach lattice, use it to generalize a result regarding the characterization of order weakly compact operators, and establish its converse. Also, we derive some interesting consequences.

Some common fixed point theorems in normed linear spaces

Alfred Olufemi Bosede (2010)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In this paper, we establish some generalizations to approximate common fixed points for selfmappings in a normed linear space using the modified Ishikawa iteration process with errors in the sense of Liu [10] and Rafiq [14]. We use a more general contractive condition than those of Rafiq [14] to establish our results. Our results, therefore, not only improve a multitude of common fixed point results in literature but also generalize some of the results of Berinde [3], Rhoades [15] and recent results...

Some properties of weak Banach-Saks operators

Othman Aboutafail, Larbi Zraoula, Noufissa Hafidi (2021)

Mathematica Bohemica

We establish necessary and sufficient conditions under which weak Banach-Saks operators are weakly compact (respectively, L-weakly compact; respectively, M-weakly compact). As consequences, we give some interesting characterizations of order continuous norm (respectively, reflexive Banach lattice).

Some results on order weakly compact operators

Belmesnaoui Aqzzouz, Jawad Hmichane (2009)

Mathematica Bohemica

We establish some properties of the class of order weakly compact operators on Banach lattices. As consequences, we obtain some characterizations of Banach lattices with order continuous norms or whose topological duals have order continuous norms.

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