Grothendieck-type subsets of Banach lattices

Galindo, Pablo; Miranda, V. C. C.

doi:10.1016/j.jmaa.2021.125570

Cited by 13 publications

(5 citation statements)

References 10 publications

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“…Section 4 is devoted to the almost Grothendieck operators. introduced recently in [29]. In Section 5, the almost Dunford-Pettis operators are studied.…”

Section: 8mentioning

confidence: 99%

Regularly limited, Grothendieck, and Dunford--Pettis operators

Alpay¹,

Emelyanov²,

Gorokhova³

2022

Preprint

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Various types of compactness in Banach spaces were in streamline of functional analysis in the second half of the 20th century. At some point, in order to diversify the classes of compact operators, the Banach lattice structure had come in play by Meyer-Nieberg, Dodds, Fremlin, Aliprantis, Wickstead, and others. In the present paper, we continue this line of study with main emphasis on regularity of operators under the investigation.

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“…Section 4 is devoted to the almost Grothendieck operators. introduced recently in [29]. In Section 5, the almost Dunford-Pettis operators are studied.…”

Section: 8mentioning

confidence: 99%

Regularly limited, Grothendieck, and Dunford--Pettis operators

Alpay¹,

Emelyanov²,

Gorokhova³

2022

Preprint

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“…Since then L-weakly compact operators and limited operators attract permanent attention and inspire researchers. Recently further related classes of operators were introduced and studied by many authors (see, for example, [2,4,7,8,10,11,12,15,18,19], and references therein). Using the Meyer-Nieberg approach for the Dunford-Pettis and for limited (instead of bounded) sets in the domain, we introduce Dunford-Pettis-Lwc and the limitedly-Lwc operators.…”

Section: Introductionmentioning

confidence: 99%

$$o\tau $$-Continuous, Lebesgue, KB, and Levi Operators Between Vector Lattices and Topological Vector Spaces

2022

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“…The lattice counterpart of this important operator ideal is the class of almost Dunford-Pettis operators: an operator from a Banach lattice to a Banach space is almost Dunford-Pettis if it sends disjoint weakly null sequences to norm null sequences; or, equivalently, if it sends positive disjoint weakly null sequences to norm null sequences. Almost Dunford-Pettis operators have attracted the attention of many experts, for recent developments see [4,5,12,13,18,20,21,22].…”

Section: Introductionmentioning

confidence: 99%

Adjoints and second adjoints of almost Dunford-Pettis operators

Botelho¹,

Garcı́a²

2022

Preprint

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We investigate when the adjoint T * and the second adjoint T * * of an operator T betweeen Banach lattices is almost Dunford-Pettis. First we show when T * * is almost Dunford-Pettis for every T . Then we prove when T * or T * * is almost Dunford-Pettis whenever T is positive and almost Dunford-Pettis. Finally we prove when T * * is an almost Dunford-Pettis operator whenever T is order weakly compact.

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Grothendieck-type subsets of Banach lattices

Cited by 13 publications

References 10 publications

Regularly limited, Grothendieck, and Dunford--Pettis operators

Regularly limited, Grothendieck, and Dunford--Pettis operators

$$o\tau $$-Continuous, Lebesgue, KB, and Levi Operators Between Vector Lattices and Topological Vector Spaces

Adjoints and second adjoints of almost Dunford-Pettis operators

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