Abstract. We characterize Banach lattices on which the class of order weakly compact operators coincides with that of weakly compact operators and we give some consequences.

AMS Subject Classification (1991): 46A40, 46B40, 46B42

Keyword(s): order weakly compact operator, weakly compact operator, order continuous norm, reflexive Banach lattice

Received July 13, 2011, and in final form April 20, 2012. (Registered under 37/2011.)