On the class of weak almost limited operators

Elbour, Aziz; Machrafi, Nabil; Moussa, Mohammed

doi:10.2989/16073606.2015.1015652

Cited by 7 publications

(7 citation statements)

References 10 publications

(10 reference statements)

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“…By [10], an operator T from X into E is said to be weak and almost limited operator, if it carries relatively weakly compact sets in X to almost limited ones.…”

Section: Order Almost Dunford-pettis Operatorsmentioning

confidence: 99%

Weak* almost Dunford-Pettis operators in Banach lattices

Ardakani¹,

Salimi²,

Mosadegh³

2014

Journal of Nonlinear Analysis and Application

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By introducing the concepts of order almost Dunford-Pettis and almost weakly limited operators in Banach lattices, we give some properties of them related to some well known classes of operators, such as, order weakly compact, order Dunford-Pettis, weak and almost Dunford-Pettis and weakly limited operators. Then, we characterize Banach lattices E and F on which each operator from E into F that is order almost Dunford-Pettis and weak almost Dunford-Pettis is an almost weakly limited operator.

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“…By [10], an operator T from X into E is said to be weak and almost limited operator, if it carries relatively weakly compact sets in X to almost limited ones.…”

Section: Order Almost Dunford-pettis Operatorsmentioning

confidence: 99%

Weak* almost Dunford-Pettis operators in Banach lattices

Ardakani¹,

Salimi²,

Mosadegh³

2014

Journal of Nonlinear Analysis and Application

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“…We acknowledge that some results of our original article have been proved earlier in [1,2] by Elbour et al…”

mentioning

confidence: 73%

“…At last, Theorem 2.1 and part of Theorem 2.6 of the original paper are contained in [2, Theorem 2.7] and [2, Corollary 2.11], respectively. We feel sorry about that we ignored [1,2].…”

mentioning

confidence: 99%

Erratum to: On positive almost weak* Dunford–Pettis operators

2015

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“…-weak almost limited (wa-limited) [9], if f n (T x n ) → 0 for all weakly null sequences (x n ) ⊂ E and all weak* null sequences (f n ) ⊂ F ′ with pairwise disjoint terms.…”

Section: Terminologymentioning

confidence: 99%

“…This note is a sequel to the recent works [9,17] where the authors introduced and characterized the class of weak almost limited operators, and investigated their relationship with almost limited (resp. almost Dunford-Pettis, weak* Dunford-Pettis) operators.…”

Section: Introductionmentioning

confidence: 97%

A note on weak almost limited operators

Machrafi¹,

Fahri²,

Moussa³

et al. 2018

HJMS

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Let us recall that an operator T : E → F, between two Banach lattices, is said to be weak* Dunford-Pettis (resp. weak almost limited) if fn (T xn) → 0 whenever (xn) converges weakly to 0 in E and (fn) converges weak* to 0 in F (resp. fn (T xn) → 0 for all weakly null sequences (xn) ⊂ E and all weak* null sequences (fn) ⊂ F with pairwise disjoint terms). In this note, we state some sufficient conditions for an operator R : G → E(resp. S : F → G), between Banach lattices, under which the product T R (resp. ST) is weak* Dunford-Pettis whenever T : E → F is an order bounded weak almost limited operator. As a consequence, we establish the coincidence of the above two classes of operators on order bounded operators, under a suitable lattice operations' sequential continuity of the spaces (resp. their duals) between which the operators are defined. We also look at the order structure of the vector space of weak almost limited operators between Banach lattices.

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On the class of weak almost limited operators

Cited by 7 publications

References 10 publications

Weak* almost Dunford-Pettis operators in Banach lattices

Weak* almost Dunford-Pettis operators in Banach lattices

Erratum to: On positive almost weak* Dunford–Pettis operators

A note on weak almost limited operators

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