Some characterizations of order weakly compact operator. (English) Zbl 1224.46035

Aqzzouz, B.; Elbour, A.

Math. Bohem. 136, No. 1, 105-112 (2011).

Summary: We introduce the notion of order weakly sequentially continuous lattice operations of a Banach lattice, use it to generalize a result regarding the characterization of order weakly compact operators, and establish its converse. We also derive some interesting consequences.

MSC:

46B42	Banach lattices
47B65	Positive linear operators and order-bounded operators

Keywords:

order weakly compact operator; order continuous norm; discrete Banach lattice; weakly sequentially continuous lattice operation