Turkish Journal of Mathematics
Abstract
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.
DOI
10.55730/1300-0098.3455
Keywords
Banach lattice, affiliated operators, enveloping norm, domination problem
First Page
1659
Last Page
1673
Recommended Citation
EMELYANOV, E, & GOROKHOVA, S (2023). Operators affiliated to Banach lattice properties and their enveloping norms. Turkish Journal of Mathematics 47 (6): 1659-1673. https://doi.org/10.55730/1300-0098.3455
