## Absolutely $(r,p,q)$-summing inclusions

### Volume 178 / 2007

Studia Mathematica 178 (2007), 19-45
MSC: 47B10, 46M35, 47B06.
DOI: 10.4064/sm178-1-2

#### Abstract

As a continuation of the work of Bennett and Carl for the case $q=\infty $, we consider absolutely $(r,p,q)$-summing inclusion maps between Minkowski sequence spaces, $1 \le p,q \le 2$. Using these results we deduce parts of the limit orders of the corresponding operator ideals and an inclusion theorem between the ideals of $(u,s,t)$-nuclear and of absolutely $(r,p,q)$-summing operators, which gives a new proof of a result of Carl on Schatten class operators. Furthermore, we also consider inclusions between arbitrary Banach sequence spaces and inclusions between finite-dimensional Schatten classes. Finally, applications to Hilbert numbers of inclusions are given.