COMPLETELY (q,p)-MIXING MAPS

摘要

Several important results for p-summing operators, such as Pietsch's composition formula and Grothendieck's theorem, share the following form: there is an operator T such that S o T is p-summing whenever S is q-summing. Such operators were called (q,p)-mixing by Pietsch, who studied them systematically. In the operator space setting, G. Pisier's completely p-summing maps correspond to the p-summing operators between Banach spaces. A natural modification of the definition yields the notion of completely (q,p)-mixing maps, already introduced by K. L. Yew, which is the subject of this paper. Some basic properties of these maps are proved, as well as a couple of characterizations. A generalization of Yew's operator space version of the Extrapolation theorem is obtained, via an interpolation-style theorem relating different completely (q,p)-mixing norms. Finally, some composition theorems for completely p-summing maps are proved.