On the positive weak almost limited operators

Erratum to: On positive almost weak* Dunford–Pettis operators

“…We acknowledge that some results of our original article have been proved earlier in [1,2] by Elbour et al…”

“…At last, Theorem 2.1 and part of Theorem 2.6 of the original paper are contained in [2, Theorem 2.7] and [2, Corollary 2.11], respectively. We feel sorry about that we ignored [1,2].…”

A note on weak almost limited operators

“…As consequense we have the following generalisation of[17, Corollary 2.11].Corollary 3.2.Let E and F be two Banach lattices such that F is σ-Dedekind complete. Then, an order bounded operator T : E → F is wa-limited if and only if it is w*DP, whenever one of the following holds:(i) E has sequentially weakly continuous lattice operations.…”

“…This note is a sequel to the recent works [9,17] where the authors introduced and characterized the class of weak almost limited operators, and investigated their relationship with almost limited (resp. almost Dunford-Pettis, weak* Dunford-Pettis) operators.…”

“…The condition (iii) is a generalisation of the assumption " F ′ has sequentially weak* continuous lattice operations " that is in[17, Corollary 2.11]. Indeed, since F is σ-Dedekind complete, the latter assumption is equivalent by[22, Theorem 6.6] to F is discrete with order continuous norm, and hence by [19, Proposition 2.5.23] F has sequentially weakly continuous lattice operations.In case F is σ-Dedekind complete and F ′ has sequentially weak* continuous lattice operations, the conclusion of Corollary 3.2 is sharpened as follows.…”