ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 66, 1 (1997)
pp. 135-147

SUPERREFLEXIVITY AND $J$-CONVEXITY OF BANACH SPACES
J. WENZEL

Abstract. 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. 46B07, 46B10
Keywords. superreflexivity, summation operator, $J$-convexity

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Acta Mathematica Universitatis Comenianae
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Comenius University
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