\(d\)-independence and \(d\)-bases
In this note the authors formulate some questions concerning the notion of a \(d\)-basis which is a convenient tool for the investigation of properties of disjointness preserving operators. Some very basic and natural questions about \(d\)-bases remain open and this might be one of the major obstacles in obtaining a complete understanding of the structure of disjointness preserving operators between vector lattices. For example, in the first problem they ask: is it true that every maximal \(d\)-independent system in an arbitrary vector lattice \(X\) is a \(d\)-basis? If \(X\) is a vector lattice with a cofinal family of projection bands, the answer is affirmative.
scientific article; zbMATH DE number 2002008