Some characterizations of KB-operators on Banach lattices and ordered Banach spaces

Authors: BİROL ALTIN, NABIL MACHRAFI

Abstract: We determine that two recent classes of KB-operators and weak KB-operators and the well-known class of b-weakly compact operators, from a Banach lattice into a Banach space, are the same. We extend our study to the ordered Banach space setting by showing that a weak chain-preserving operator between two ordered Banach spaces is a KB-operator if and only if it is a weak KB-operator.

Keywords: KB-operator, b-weakly compact operator, Banach lattice, ordered Banach space, normal cone

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