As a continuation of the work of Bennett and Carl for the case q = ∞, we consider absolutely (r,p,q)-summing inclusion maps between Minkowski sequence spaces, 1 ≤ p,q ≤ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-1-2,
author = {Carsten Michels},
title = {Absolutely (r,p,q)-summing inclusions},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {19-45},
zbl = {1112.47014},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-1-2}
}
Carsten Michels. Absolutely (r,p,q)-summing inclusions. Studia Mathematica, Tome 178 (2007) pp. 19-45. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-1-2/