Uniform non-$\ell^n_1$-ness of $\ell_\infty$-sums of Banach spaces

ArticleOriginal scientific text

Title

Authors ,

We shall characterize the uniform non-

ℓ_{1}^{n}

-ness of

ℓ_{\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.

ℓ_{\infty}

-sum of Banach spaces, uniformly non-square space, uniformly non-

ℓ_{1}^{n}

-space, super-reflexivity, fixed point property, constant

R (a, X)

.