Several recent papers were devoted to various modifications of limited, Grothendieck, and Dunford-Pettis operators, etc., through involving the Banach lattice structure. In the present paper, it is shown that many of these operators appear as operators affiliated to well-known properties of Banach lattices, like the disjoint (dual) Schur property, the disjoint Grothendieck property, the property (d), the sequential w$^\ast$-continuity of the lattice operations, etc. We also introduce new classes of operators such as the s-GPP-operators, s-BDP-operators, and bi-sP-operators. It is proved that the spaces consisting of regular versions of the above-mentioned operators are all the Banach spaces. The domination problem for these operators is investigated.
Banach lattice, affiliated operators, enveloping norm, domination problem
EMELYANOV, EDUARD and GOROKHOVA, SVETLANA
"Operators affiliated to Banach lattice properties and their enveloping norms,"
Turkish Journal of Mathematics: Vol. 47:
6, Article 5.
Available at: https://journals.tubitak.gov.tr/math/vol47/iss6/5