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

Mikio Kato, and Takayuki Tamura. "Uniform non-$\ell ^n_1$-ness of $\ell _\infty $-sums of Banach spaces." Commentationes Mathematicae 49.2 (2009): null. <http://eudml.org/doc/292028>.

@article{MikioKato2009,
abstract = {We shall characterize the uniform non-$\ell ^n_1$-ness of $\ell _\infty $-sums of Banach spaces $(X_1 \oplus \dots \oplus X_m)_\infty $. As applications, some results on super-reflexivity and the fixed point property for nonexpansive mappings will be presented.},
author = {Mikio Kato, Takayuki Tamura},
journal = {Commentationes Mathematicae},
keywords = {$\ell _\infty $-sum of Banach spaces; uniformly non-square space; uniformly non-$\ell ^n_1$-space, super-reflexivity; fixed point property; constant $R(a, X)$.},
language = {eng},
number = {2},
pages = {null},
title = {Uniform non-$\ell ^n_1$-ness of $\ell _\infty $-sums of Banach spaces},
url = {http://eudml.org/doc/292028},
volume = {49},
year = {2009},
}

TY - JOUR
AU - Mikio Kato
AU - Takayuki Tamura
TI - Uniform non-$\ell ^n_1$-ness of $\ell _\infty $-sums of Banach spaces
JO - Commentationes Mathematicae
PY - 2009
VL - 49
IS - 2
SP - null
AB - We shall characterize the uniform non-$\ell ^n_1$-ness of $\ell _\infty $-sums of Banach spaces $(X_1 \oplus \dots \oplus X_m)_\infty $. As applications, some results on super-reflexivity and the fixed point property for nonexpansive mappings will be presented.
LA - eng
KW - $\ell _\infty $-sum of Banach spaces; uniformly non-square space; uniformly non-$\ell ^n_1$-space, super-reflexivity; fixed point property; constant $R(a, X)$.
UR - http://eudml.org/doc/292028
ER -