Some results on unbounded absolute weak Dunford–Pettis operators

A continuous operator T between two normed vector lattices E and F is called unbounded order-norm continuous whenever x? uo? 0 implies ||Tx?|| ? 0, for each norm bounded net (x?)? ? E. Let E and F be two Banach lattices. A continuous operator T : E ? F is called unbounded norm continuous, if for each norm bounded net (x?)? ? E, x? un? 0 implies Tx? un? 0. In this manuscript, we study some properties of these classes of operators and investigate their relationships with the other classes of operators.

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“…2 ⇒ 3 By assumption and Proposition 3.3, each compact operator is uaw-Dunford-Pettis. Then by Theorem 3.1 of [15] the proof is complete.…”

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confidence: 75%

Unbounded order-norm continuous and unbounded norm continuous operator

Azar

Matin

Alavizadeh

2021

Filomat

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“…In the section 2, it is clear that uaw-Dunford-Pettis operator is σ-scontinuous, moreover it is σ-un-continuous. Similar to [11], we describe Banach lattice by the "weaker" operator.…”

Section: Characterization Of Banach Lattice By These Operators and Cl...mentioning

confidence: 99%

“…The compact operators based on unbounded convergence has been investigated in [7,10]. Recently, unbounded order continuous operator and uaw-Dunford-Pettis operator are also studied in [9,10,11]. Now, we consider the continuous operators based on unbounded topology convergence.…”

Section: Introductionmentioning

confidence: 99%

Continuous operators for unbounded convergence in Banach lattices

Wang¹,

Chen²,

Chen³

2019

Preprint

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In this paper, using the unbounded norm convergence in Banach lattices, we define and investigate a new classes of operators, named strong continuous operators and unbounded norm continuous operators. We first study the relationship with the original operators, also we characterize order continuous, KB and reflexive Banach lattices by these operators, we research the space generated by these operators in final.

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“…These operators are introduced and examined in [15], the class of all uaw-Dounford-Pettis operators on E will be denoted by B U DP (E). This is continued in [10]. Moreover if F is a Banach lattice, a continuous operator T : E → F is said to be • un-continuous if for every norm bounded and un-null net (x α ) ⊆ E, T (x α ) un − → 0 in F .…”

Section: Introductionmentioning

confidence: 99%

Weak Unbounded Norm Topology and Dounford-Pettis Operators

Matin,

Azar,

Alavizadeh

2020

Preprint

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In this paper, we study un-dual (in symbol, E ⋄ ) of Banach lattice E and compare it with topological dual E * . If E * has order continuous norm, then E * = E ⋄ . We introduce and study weakly unbounded norm topology (wun-topology) on Banach lattices and compare it with weak topology and uaw-topology. In the final, we introduce and study wun-Dunford-Pettis opertors from a Banach lattice E into Banach space X and we investigate some of its properties and its relationships with others known operators.

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Some results on unbounded absolute weak Dunford–Pettis operators

Abstract: In this paper, we characterize Banach lattices on which each Dunford-Pettis operator (or weak Dunford-Pettis) is unbounded absolute weak Dunford-Pettis operator and the converse.

Cited by 6 publications

References 18 publications

Unbounded order-norm continuous and unbounded norm continuous operator

Unbounded order-norm continuous and unbounded norm continuous operator

Continuous operators for unbounded convergence in Banach lattices

Weak Unbounded Norm Topology and Dounford-Pettis Operators

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