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

Carsten Michels¹

¹ Department of Mathematics University of Oldenburg Postfach 2503 D-26111 Oldenburg, Germany

Studia Mathematica, Tome 178 (2007) no. 1, pp. 19-45

Résumé

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.

Détail

DOI : 10.4064/sm178-1-2

Keywords: continuation work bennett carl infty consider absolutely summing inclusion maps between minkowski sequence spaces using these results deduce parts limit orders corresponding operator ideals inclusion theorem between ideals nuclear absolutely summing operators which gives proof result carl schatten class operators furthermore consider inclusions between arbitrary banach sequence spaces inclusions between finite dimensional schatten classes finally applications hilbert numbers inclusions given