Banach lattices of continuous Banach lattice-valued functions
The Banach lattices of scalar-valued continuous functions on compact or locally compact Hausdorff spaces are the important objects both in their own right and also as the tools of studying the underlying topological spaces. In the paper under review, the authors introduce and study the vector-valued analogues of such vector lattices, having a Banach lattice as a range space. In particular, they study various kinds of order completeness and the classical relationships between the order and the norm. They also describe the center of these new spaces. We refer for exact definitions and statements to this interesting work. Notice in conclusion that the paper continues and expands a line of investigation, the authors started in their previous paper [Turk. J. Math. 18, 272-279 (1994)].
Banach lattices of scalar-valued continuous functions
scientific article; zbMATH DE number 902491