The 𝑉₀ property in Banach Lattices

Abstract

Order weakly compact and order unconditionally converging operators are consider on the setting of Banach latices. In this paper we characterize the class of Banach lattices on which o-weakly compact operators on it are order unconditionally converging operators. Two class of Banach having the V₀ property is showing. We also consider the spaces E on which every âŽ¸ðœŽ ⎸(E”², E)-convergent sequences on E”² are ðœŽ(E”², E”³) -convergent.