We lift to homogeneous polynomials and multilinear mappings a linear result due to Lindenstrauss and Pełczyński for absolutely summing operators. We explore the notion of cotype to obtain stronger results and provide various examples of situations in which the space of absolutely summing homogeneous polynomials is different from the whole space of homogeneous polynomials. Among other consequences, these results enable us to obtain answers to some open questions about absolutely summing homogeneous polynomials and multilinear mappings on spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm157-2-2,
author = {Daniel Pellegrino},
title = {Cotype and absolutely summing homogeneous polynomials in $L\_{p}$ spaces},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {121-131},
zbl = {1031.46052},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm157-2-2}
}
Daniel Pellegrino. Cotype and absolutely summing homogeneous polynomials in $ℒ_{p}$ spaces. Studia Mathematica, Tome 157 (2003) pp. 121-131. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm157-2-2/