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Summary: Houston Journal of Mathematics
c 2011 University of Houston
Volume 37, No. 3, 2011
ON BANACH SPACES CONTAINING lp OR c0
GEORGE ANDROULAKIS, NIGEL KALTON, AND ADI TCACIUC
Communicated by William B. Johnson
Abstract. We use the Gowers block Ramsey theorem to characterize Ba-
nach spaces containing isomorphs of p (for some 1 p < ) or c0.
1. Introduction
A result of Zippin [Z] gives a characterization of the unit vector basis of c0
and lp. He showed that a normalized basis of a Banach space such that all
normalized block bases are equivalent, must be equivalent to the unit vector basis
of c0 or lp for some 1 p < . Let 1 p A Banach space X with a
basis (xi)i is called asymptotic-lp (asymptotic-c0 if p = ) [M-TJ] if there exists
K > 0 and an increasing function f : N N such that, for all n, if (yi)n
i=1 is a
normalized block basis of (xi)
i=f(n), then (yi)n
i=1 is equivalent to the unit vector
basis of ln
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