Duality Properties for $\mathrm{b}$-$\mathrm{AM}$-Compact Operators on Banach Lattices

We obtain some necessary and some sufficient conditions on Banach lattices $E$ and $F$ such that (i) if $T\colon E\to F$ is a $\mathrm{b}$-$\mathrm{AM}$-compact operator, then $T'\colon F'\to E'$ is also $\mathrm{b}$-$\mathrm{AM}$-compact operator and (ii) if $T'\colon F'\to E'$ is $\mathrm{b}$-$\mathrm{AM}$-compact operator, then $T\colon E\to F$ is also $\mathrm{b}$-$\mathrm{AM}$-compact operator.