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.
KB-operator, b-weakly compact operator, Banach lattice, ordered Banach space, normal cone
ALTIN, BİROL and MACHRAFI, NABIL
"Some characterizations of KB-operators on Banach lattices and ordered Banach spaces,"
Turkish Journal of Mathematics: Vol. 44:
5, Article 16.
Available at: https://journals.tubitak.gov.tr/math/vol44/iss5/16