Sums of order bounded disjointness preserving linear operators (Q2002488)

The authors study the possibility of decomposing an order bounded $n$-disjoint operator into a sum of disjointness preserving operators. It turns out that such a decomposition is unique up to some ``Boolea- valued permutation''. Namely, the authors define a purely $n$-disjoint linear operator $T : E \to F$ between real vector lattices $E$ and $F$ if $n$ is the least natural for which $T$ is $n$-disjoint for all nonzero band projections in the second annihilator of $T(E)$. This concept proves fruitful for formulating the Boolean-valued analogue of permutations that yield the desired decompositions.