The class of demi KB-operators on Banach lattices

: In this paper, we introduce and study the new concept of demi KB-operators. Let E be a Banach lattice. An operator T : E −→ E is said to be a demi KB-operator if, for every positive increasing sequence { x n } in the closed unit ball B E of E such that { x n − Tx n } is norm convergent to x ∈ E , there is a norm convergent subsequence of { x n } . If the latter sequence has a weakly convergent subsequence then T is called a weak demi KB-operator. We also investigate the relationship of these classes of operators with classical notions of operators, such as b-weakly demicompact operators and demi Dunford-Pettis operators.