Canad. Math. Bull. 54(2011), 577-579
Printed: Dec 2011
It is proved that if a positive operator
$S: E \rightarrow F$ is AM-compact whenever its adjoint
$S': F' \rightarrow E'$ is AM-compact, then either the
norm of F is order continuous or $E'$ is discrete.
This note corrects an error in the proof of Theorem 2.3 of
B. Aqzzouz, R. Nouira, and L. Zraoula, The duality problem for
the class of AM-compact operators on Banach lattices. Canad. Math. Bull.
46A40 - Ordered topological linear spaces, vector lattices [See also 06F20, 46B40, 46B42]
46B40 - Ordered normed spaces [See also 46A40, 46B42]
46B42 - Banach lattices [See also 46A40, 46B40]