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Uniform non-\(\ell_1^n\)-ness of \(\ell_1\)-sums of Banach spaces

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Kato M., Tamura T.

Commentationes Mathematicae

2007

tom 47

nr 2

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.

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1 Commentationes Mathematicae

1 Kato M.

1 Tamura T.

1 2007

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Uniform non-\(\ell_1^n\)-ness of \(\ell_1\)-sums of Banach spaces