On the class of order L-weakly and order M-weakly compact operators

Lhaimer, Driss; Bouras, Khalid; Moussa, Mohammed

doi:10.1007/s11117-021-00829-2

Cited by 12 publications

(15 citation statements)

References 5 publications

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“…The scheme described in the previous subsection applied to A = T (C) with any w-compact subset C of X and to B = B F ′ produces almost LW-and almost MW-operators [14], whereas the choice of A = T ([−x, x]) with arbitrary x ∈ E + and B = B F ′ produces order LW-and order MWoperators [27]. Taking in the scheme A = T (C) with any compact C ⊆ X and B = B F ′ gives:…”

Section: 4mentioning

confidence: 99%

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Generalizations of L- and M-weakly compact operators

Alpay¹,

Emelyanov²,

Gorokhova³

2022

Preprint

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L-and M-weakly compact operators were introduced by Meyer-Nieberg in the beginning of 70th in attempts of a diversification of the concept of weakly compact operators via imposing Banach lattice structure on the range or on the domain of operators. We investigate regularity and algebraic properties of several generalizations of L-and M-weakly compact operators from the unified point of view with main focus on almost (order) L-, M-weakly compact operators, which were introduced recently by Bouras, Lhaimer, and Moussa. We also study several disjoint sequence properties in Banach lattices: the property (d), the dual disjoint Schur property, and the disjoint Grothendieck property.

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Section: 4mentioning

confidence: 99%

“…For further unexplained terminology and notations, we refer to [3,4,6,7,9,14,22,23,27,28,33,34,35,36].…”

Section: For Anymentioning

confidence: 99%

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Generalizations of L- and M-weakly compact operators

Alpay¹,

Emelyanov²,

Gorokhova³

2022

Preprint

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“…Weakly compact operators, L-weakly compact operators, M-weakly compact operators and order L-weakly compact operators are all order weakly compact (see [2, Sections 5.2 and 5.3, Theorem 5.61 and p. 319] and [14]), so Theorem 5.1 applies to all these kinds of operators. As to the condition on the Banach lattice E, it is clear that bounded sequences on C(K), where K is a compact Hausdorff space, are order bounded.…”

Section: The Role Of Weak Compactnessmentioning

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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“…In general, the implications in Assertion 1.6.7(ii) and in Assertion 1.6.8(ii) are proper (see [13,Rem.2.1] and [35,Rem.2.3]). As an immediate consequence of Assertions 1.6.6, 1.6.7, and 1.6.8 we have the following (semi-) bi-duality.…”

Section: 6mentioning

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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On the class of order L-weakly and order M-weakly compact operators

Cited by 12 publications

References 5 publications

Generalizations of L- and M-weakly compact operators

Generalizations of L- and M-weakly compact operators

Adjoints and second adjoints of almost Dunford-Pettis operators

Regularly limited, Grothendieck, and Dunford--Pettis operators

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