Aspects of (pq) summing multipliers

Abstract

A sequence (uj)j2N of operators in L(X; Y ) is a (p; q)-summing multi- plier (or (p; q)-summing sequence of operators), in short (uj) 2 `¼p;q (X; Y ), if there exists a constant C > 0 such that, for any ¯nite collection of vectors x1; x2; : : : xn in X, it holds that ³ n Xj=1 kujxjkp´1=p · C sup n³ n Xj=1 jx¤xj jq´1=q ; x¤ 2 BX¤o: Some examples of these operators, inclusions between the spaces and connections with spaces of multipliers are presented.¤ Mathematics Subject Classi¯cation (2000): 47B10.