Incompleteness of the linear span of the positive compact operators

Wickstead, Anthony; Chen, Z.L.

doi:10.1090/s0002-9939-97-04220-2

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1998

2024

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Cited by 14 publications

(1 citation statement)

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“…In general, quite a little is known about conditions on P-operators under which every regular P-operator is an r-P-operator, even for compact operators in a Banach lattice (see [16,18], where the space of r-compact operators from E to F is denoted by K r (E, F ), and references therein). By [1,Thm.4(ii)], there exists a compactly dominated compact operator on…”

Section: 5mentioning

confidence: 99%

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: 5mentioning

confidence: 99%