(p, q)-Summing Sequences of Operators

Abstract

A sequence (u _j)_j∈N of operators inL (X, Y) is a (p, q)-summing multiplier (or (p, q)-summing sequence of operators), in short (u _j) ∈l _{πp, q} (X, Y), if there exists a constant C > 0 such that, for any finite collection of vectors _{x 1} , x ₂ ,... x _n in X, it holds that