Cotype and absolutely summing homogeneous polynomials in ${ℒ}_p$ spaces

Daniel Pellegrino. "Cotype and absolutely summing homogeneous polynomials in $ℒ_{p}$ spaces." Studia Mathematica 157.2 (2003): 121-131. <http://eudml.org/doc/284598>.

@article{DanielPellegrino2003,
abstract = {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 $ℒ_\{∞\}$ spaces.},
author = {Daniel Pellegrino},
journal = {Studia Mathematica},
keywords = {-summing polynomial; finite factorisation; cotype},
language = {eng},
number = {2},
pages = {121-131},
title = {Cotype and absolutely summing homogeneous polynomials in $ℒ_\{p\}$ spaces},
url = {http://eudml.org/doc/284598},
volume = {157},
year = {2003},
}

TY - JOUR
AU - Daniel Pellegrino
TI - Cotype and absolutely summing homogeneous polynomials in $ℒ_{p}$ spaces
JO - Studia Mathematica
PY - 2003
VL - 157
IS - 2
SP - 121
EP - 131
AB - 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 $ℒ_{∞}$ spaces.
LA - eng
KW - -summing polynomial; finite factorisation; cotype
UR - http://eudml.org/doc/284598
ER -