Abstract. We study the compactness of $b$-weakly compact operators. As a consequence, we characterize Banach lattices for which the class of $b$-AM-compact operators coincides with that of compact operators (resp. weakly compact operators).

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

Keyword(s): order continuous norm, Schur property, $b$-AM-compact operator, compact operator, $b$-weakly compact operator

Received November 15, 2010, and in revised form December 22, 2010. (Registered under 81/2010.)