On Schwartz Operator Ideals Determined by the Order-Bounded Sets in a Banach Lattice

摘要

The p-nuclear operators are characterized as those operators factoring through l(p) for which one factor is strongly majorizing. Likewise the applications of p-nuclear are characterized as those l(p) factorizable operators for which one factor is cone absolutely summing. Results are obtained in the general setting of Schwartz operator ideals, and consequently it is possible to generalize the notions 'p-nuclear' and 'absolutely p-summing' to 'H-nuclear' and 'absolutely H-summing', where H is an arbitrary Banach lattice.