In this paper, we introduce and investigate new concepts of L-weakly M-weakly demicompact operators. Let E be a Banach lattice. An operator T : ? is called demicompact, if for every norm bounded sequence (xn) in BE such that {xn Txn, n N} an compact subset E, have {xn, E. Additionally, disjoint ?xn ?Txn? 0, ?xn? 0. (resp. M-weakly) operators generalize known classes which are We also elaborate ...

W. L. Bynum introduced the weakly convergent sequence coefficient WCS(A') of the Banach space X as WCS(Jf) = sup{M: for each weakly convergent sequence {xn} in X , there is some y e co({x«}) such that M • lim sup ||x,, y\\ < A({x„})} . We consider the weakly convergent sequence coefficient of the /^-product space Z = (fTjLi Xi)t of tne finite non-Schur space Xx, ... , X„ and show that WCS(Z) = ...