A problem on spreading models

Details A problem on spreading models A problem on spreading models

1996-07-12

arxiv.org/abs/math/9607207v1

Mathematics

Functional Analysis

Scientific paper

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 $\ell_1$ (respectively, $c_0$) then $X$ contains $\ell_1$ (respectively, $c_0$). 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 $\ell_1$. An equivalent norm is constructed on $T$ so that $\|s_1+s_2\|<2$ whenever $(s_n)$ is a spreading model of a normalized basic sequence in $T$.

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