Uniform non-${\ell }_1^n$-ness of ${\ell }_1$-sums of Banach spaces

Mikio Kato, and Takayuki Tamura. "Uniform non-$\ell _1^n$-ness of $\ell _1$-sums of Banach spaces." Commentationes Mathematicae 47.2 (2007): null. <http://eudml.org/doc/291796>.

@article{MikioKato2007,
abstract = {We shall characterize the uniform non-$\ell _1^n$-ness of the $\ell _1$-sum $(X_1 \oplus \dots \oplus X_m)_1$ of a finite number of Banach spaces $X_1 ,\dots , X_m$. Also we shall obtain that $(X_1 \oplus \dots \oplus X_m)_1$ is uniformly non-$\ell _1^\{m+1\}$ if and only if all $X_1 ,\dots , X_m$ are uniformly non-square (note that $(X_1 \oplus \dots \oplus X_m)_1$ is not uniformly non-$\ell _1^m$). Several related results will be presented.},
author = {Mikio Kato, Takayuki Tamura},
journal = {Commentationes Mathematicae},
keywords = {$\ell _1$-sum of Banach spaces; uniformly non-square space; uniformly non-$\ell _1^n$-space; super-reflexivity; fixed point property},
language = {eng},
number = {2},
pages = {null},
title = {Uniform non-$\ell _1^n$-ness of $\ell _1$-sums of Banach spaces},
url = {http://eudml.org/doc/291796},
volume = {47},
year = {2007},
}

TY - JOUR
AU - Mikio Kato
AU - Takayuki Tamura
TI - Uniform non-$\ell _1^n$-ness of $\ell _1$-sums of Banach spaces
JO - Commentationes Mathematicae
PY - 2007
VL - 47
IS - 2
SP - null
AB - We shall characterize the uniform non-$\ell _1^n$-ness of the $\ell _1$-sum $(X_1 \oplus \dots \oplus X_m)_1$ of a finite number of Banach spaces $X_1 ,\dots , X_m$. Also we shall obtain that $(X_1 \oplus \dots \oplus X_m)_1$ is uniformly non-$\ell _1^{m+1}$ if and only if all $X_1 ,\dots , X_m$ are uniformly non-square (note that $(X_1 \oplus \dots \oplus X_m)_1$ is not uniformly non-$\ell _1^m$). Several related results will be presented.
LA - eng
KW - $\ell _1$-sum of Banach spaces; uniformly non-square space; uniformly non-$\ell _1^n$-space; super-reflexivity; fixed point property
UR - http://eudml.org/doc/291796
ER -