We introduce and investigate the non-n-linear concept of fully summing mappings; if n = 1 this concept coincides with the notion of nonlinear absolutely summing mappings and in this sense this article unifies these two theories. We also introduce a non-n-linear definition of Hilbert-Schmidt mappings and sketch connections between this concept and fully summing mappings.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-1-3,
author = {M\'ario C. Matos and Daniel M. Pellegrino},
title = {Fully summing mappings between Banach spaces},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {47-61},
zbl = {1117.46052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-1-3}
}
Mário C. Matos; Daniel M. Pellegrino. Fully summing mappings between Banach spaces. Studia Mathematica, Tome 178 (2007) pp. 47-61. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-1-3/