A Problem on Spreading Models
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It is proved that if a Banach spaceXhas a basis (en) satisfying every spreading model of a normalized block basis of (en) is 1-equivalent to the unit vector basis of ℓ1 (respectively,c0) thenXcontains ℓ1(respectively,c0). Furthermore, Tsirelson's spaceTis shown to have the property that every infinite dimensional subspace contains a sequence having spreading model 1-equivalent to the unit vector basis of ℓ1. An equivalent norm is constructed onTso that s1+s2<2 whenever (sn) is a spreading model of a normalized basic sequence inT. © 1998 Academic Press.
author list (cited authors)
Odell, E., & Schlumprecht, T. h.