A problem on spreading models

1996/07/12 by Odell, Edward, Schlumprecht, Thomas
#46B45 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.math/9607207

Abstract

It is proved that if a Banach space X has a basis (e_n) satisfying every spreading model of a normalized block basis of (e_n) is 1-equivalent to the unit vector basis of ℓ₁ (respectively, c₀) then X contains ℓ₁ (respectively, c₀). Furthermore Tsirelson's space T is 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 on T so that ‖s₁+s₂‖<2 whenever (s_n) is a spreading model of a normalized basic sequence in T.

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