Abstract. We investigate some properties of the class of semi-compact operators on Banach lattices and we give some interesting consequences. In particular we are interested in Banach lattices $E$ and $F$ such that (a) every order bounded operator $T\colon E\rightarrow F$ possessing a semi-compact adjoint is semi-compact as well, (b) every order bounded semi-compact operator $T\colon E\rightarrow F$ has a semi-compact adjoint.

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

Keyword(s): semi-compact operator, order continuous norm, discrete Banach lattice

Received March 5, 2010, and in revised form May 10, 2010. (Registered under 18/2010.)