The inclusion theorem for multiple summing operators

David Pérez-García. "The inclusion theorem for multiple summing operators." Studia Mathematica 165.3 (2004): 275-290. <http://eudml.org/doc/285066>.

@article{DavidPérez2004,
abstract = {We prove that, for 1 ≤ p ≤ q < 2, each multiple p-summing multilinear operator between Banach spaces is also q-summing. We also give an improvement of this result for an image space of cotype 2. As a consequence, we obtain a characterization of Hilbert-Schmidt multilinear operators similar to the linear one given by A. Pełczyński in 1967. We also give a multilinear generalization of Grothendieck's Theorem for GT spaces.},
author = {David Pérez-García},
journal = {Studia Mathematica},
keywords = {Hilbert-Schmidt operators; -summing operators; absolutely summing operators; multilinear operators; Grothendieck's theorem},
language = {eng},
number = {3},
pages = {275-290},
title = {The inclusion theorem for multiple summing operators},
url = {http://eudml.org/doc/285066},
volume = {165},
year = {2004},
}

TY - JOUR
AU - David Pérez-García
TI - The inclusion theorem for multiple summing operators
JO - Studia Mathematica
PY - 2004
VL - 165
IS - 3
SP - 275
EP - 290
AB - We prove that, for 1 ≤ p ≤ q < 2, each multiple p-summing multilinear operator between Banach spaces is also q-summing. We also give an improvement of this result for an image space of cotype 2. As a consequence, we obtain a characterization of Hilbert-Schmidt multilinear operators similar to the linear one given by A. Pełczyński in 1967. We also give a multilinear generalization of Grothendieck's Theorem for GT spaces.
LA - eng
KW - Hilbert-Schmidt operators; -summing operators; absolutely summing operators; multilinear operators; Grothendieck's theorem
UR - http://eudml.org/doc/285066
ER -