ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. 66,   1   (1997)
SUPERREFLEXIVITY AND $J$-CONVEXITY OF BANACH SPACES
A Banach space $X$ is superreflexive if each Banach space $Y$ that is finitely representable in $X$ is reflexive. Superreflexivity is known to be equivalent to $J$-convexity and to the non-existence of uniformly bounded factorizations of the summation operators $S_n$ through $X$. We give a quantitative formulation of this equivalence. This can in particular be used to find a factorization of $S_n$ through $X$, given a factorization of $S_N$ through $[L_2,X]$, where $N$ is `large' compared to $n$.
AMS subject classification.
superreflexivity, summation operator, $J$-convexity
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