On the modulus of disjointness-preserving operators and b-AM-compact operators on Banach lattices

Abstract

We study several properties of the modulus of order bounded disjointness-preserving operators. We show that, if $T$ is an order bounded disjointness-preserving operator, then $T$ and $\left|T\right|$ have the same compactness property for several types of compactness. Finally, we characterize Banach lattices having $b$-$\mathit{AM}$-compact (resp., $\mathit{AM}$-compact) operators defined between them as having a modulus that is $b$-$\mathit{AM}$-compact (resp., $\mathit{AM}$-compact).