By introducing the concepts of order almost Dunford-Pettis and almost weakly limited operators in Banach lattices, we give some properties of them related to some well known classes of operators, such as, order weakly compact, order Dunford-Pettis, weak and almost Dunford- Pettis and weakly limited operators. Then, we characterize Banach lat- tices E and F on which each operator from E into F t...

In this paper we give some necessary and sufficient conditions for which each Banach lattice  is    space and we study some properties of b-weakly compact operators from a Banach lattice  into a Banach space . We show that every weakly compact operator from a Banach lattice  into a Banach space  is b-weakly compact and give a counterexample which shows that the inverse is not true but we prove ...

An operator T : E → X between a Banach lattice E and a Banach space X is called b-weakly compact if T (B) is relatively weakly compact for each b-bounded set B in E. We characterize b-weakly compact operators among o-weakly compact operators. We show summing operators are b-weakly compact and discuss relation between Dunford–Pettis and b-weakly compact operators. We give necessary conditions fo...

Any Lipschitz map $f : M \to N$ between two pointed metric spaces may be extended in a unique way to bounded linear operator $\widehat {f} \mathcal {F}(M) {F}(N)$ their corresponding Lipschitz-free spaces. In this paper, we give necessary and sufficient condition for {f}$ compact terms of conditions on $f$ . This extends result by A. Jiménez-Vargas M. Villegas-Vallecillos the case non-separable...