Ya. Abramovich et Aw. Wickstead, SOLUTIONS OF SEVERAL PROBLEMS IN THE THEORY OF COMPACT POSITIVE OPERATORS, Proceedings of the American Mathematical Society, 123(10), 1995, pp. 3021-3026
We construct a compactly dominated compact operator S on a Dedekind co
mplete Banach lattice whose modulus \S\ is not compact. We also constr
uct a compactly dominated compact operator without modulus.