Multiple summing operators on $l_p$ spaces

Dumitru Popa. "Multiple summing operators on $l_{p}$ spaces." Studia Mathematica 225.1 (2014): 9-28. <http://eudml.org/doc/285765>.

@article{DumitruPopa2014,
abstract = {We use the Maurey-Rosenthal factorization theorem to obtain a new characterization of multiple 2-summing operators on a product of $l_\{p\}$ spaces. This characterization is used to show that multiple s-summing operators on a product of $l_\{p\}$ spaces with values in a Hilbert space are characterized by the boundedness of a natural multilinear functional (1 ≤ s ≤ 2). We use these results to show that there exist many natural multiple s-summing operators $T: l_\{4/3\} × l_\{4/3\} → l₂$ such that none of the associated linear operators is s-summing (1 ≤ s ≤ 2). Further we show that if n ≥ 2, there exist natural bounded multilinear operators $T: l_\{2n/(n+1)\} × ⋯ × l_\{2n/(n+1)\} → l₂$ for which none of the associated multilinear operators is multiple s-summing (1 ≤ s ≤ 2).},
author = {Dumitru Popa},
journal = {Studia Mathematica},
keywords = {-summing operators; multilinear operators; multiple summing operators; Hilbert-Schmidt operators; nuclear operators},
language = {eng},
number = {1},
pages = {9-28},
title = {Multiple summing operators on $l_\{p\}$ spaces},
url = {http://eudml.org/doc/285765},
volume = {225},
year = {2014},
}

TY - JOUR
AU - Dumitru Popa
TI - Multiple summing operators on $l_{p}$ spaces
JO - Studia Mathematica
PY - 2014
VL - 225
IS - 1
SP - 9
EP - 28
AB - We use the Maurey-Rosenthal factorization theorem to obtain a new characterization of multiple 2-summing operators on a product of $l_{p}$ spaces. This characterization is used to show that multiple s-summing operators on a product of $l_{p}$ spaces with values in a Hilbert space are characterized by the boundedness of a natural multilinear functional (1 ≤ s ≤ 2). We use these results to show that there exist many natural multiple s-summing operators $T: l_{4/3} × l_{4/3} → l₂$ such that none of the associated linear operators is s-summing (1 ≤ s ≤ 2). Further we show that if n ≥ 2, there exist natural bounded multilinear operators $T: l_{2n/(n+1)} × ⋯ × l_{2n/(n+1)} → l₂$ for which none of the associated multilinear operators is multiple s-summing (1 ≤ s ≤ 2).
LA - eng
KW - -summing operators; multilinear operators; multiple summing operators; Hilbert-Schmidt operators; nuclear operators
UR - http://eudml.org/doc/285765
ER -