Compact disjointness preserving operators (Q1316817)

Let \(X\) and \(Y\) be Banach lattices. A linear operator \(T: X\to Y\) is said to be a \(d\)-homomorphism if it maps disjoint elements to disjoint elements. The main result: If \(T: X\to Y\) is a compact \(d\)-homomorphism then there exist uniquely determined at most countable families \(\{\delta_ j\}\), \(\{y_ j\}\) of pairwise disjoint atoms in \(X^*(Y)\) such that \(T= \sum_ j \delta_ j\otimes y_ j\) (in the norm topology).