Abstract. We investigate Banach lattices on which each semi-compact operator (resp. the second power of each semi-compact operator) is $b$-weakly compact.

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

Keyword(s): semi-compact operator, $b$-weakly compact operator, order continuous norm, KB-space

Received May 11, 2009, and in revised form June 26, 2009. (Registered under 67/2009.)