•  
  •  
 

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

Plum Print visual indicator of research metrics
PlumX Metrics
  • Citations
    • Citation Indexes: 1
  • Usage
    • Downloads: 226
    • Abstract Views: 122
see details

Included in

Mathematics Commons

Share

COinS