The positive Schur property on positive projective tensor products and spaces of regular multilinear operators

The positive polynomial Schur property in Banach lattices

“…According to [10], a Banach lattice F is positively isomorphic to a subspace of the Banach lattice E if there exists a positive operator from F to E that is an into isomorphism (in the sense of Banach spaces). Proposition 2.5.…”

“…The main result of this section reads as follows. [10]). So, there exists a positive non-norm null weakly null sequence in E 1 ⊗ |π| • • • ⊗ |π| E n .…”

“…In the setting of Banach lattices, the positive Schur property (weakly null sequences formed by positive vectors are norm null) has been extensively studied, recent developments can be found in [5,8,10,16,33,36,37]. So it is a natural step to consider the lattice counterpart of the polynomial Schur property, which is the main subject of this paper.…”

Adjoints and second adjoints of almost Dunford-Pettis operators

“…The lattice counterpart of this important operator ideal is the class of almost Dunford-Pettis operators: an operator from a Banach lattice to a Banach space is almost Dunford-Pettis if it sends disjoint weakly null sequences to norm null sequences; or, equivalently, if it sends positive disjoint weakly null sequences to norm null sequences. Almost Dunford-Pettis operators have attracted the attention of many experts, for recent developments see [4,5,12,13,18,20,21,22].…”

Complete latticeability in vector-valued sequence spaces

“…The positive Schur property in Banach lattices (positive -or, equivalently, disjointweakly null sequences are norm null) was introduced by Wnuk [29] and Räbiger [27] and has been extensively studied, for some recent developments see [4,8,9,14,28,31,32]. Oikhberg [25] coined the following terms: a subset A of a Banach lattice is latticeable (completely latticeable) if there exists a (closed) infinite dimensional sublattice of E all of whose elements but the origin belong to A (see also [26]).…”