# Uniform non-${\ell}_{1}^{n}$-ness of ${\ell}_{1}$-sums of Banach spaces

Commentationes Mathematicae (2007)

- Volume: 47, Issue: 2
- ISSN: 2080-1211

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topMikio 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 -

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