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arXiv · 1502.05753

Proximity to $\ell_p$ and $c_0$ in Banach spaces

Ryan Causey
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Abstract

We construct a class of minimal trees and use these trees to establish a number of coloring theorems on general trees. Among the applications of these trees and coloring theorems are quantification of the Bourgain $\ell_p$ and $c_0$ indices, dualization of the Bourgain $c_0$ index, establishing sharp positive and negative results for constant reduction, and estimating the Bourgain $\ell_p$ index of an arbitrary Banach space $X$ in terms of a subspace $Y$ and the quotient $X/Y$.

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Ryan Causey. 2015-02-20. Proximity to $\ell_p$ and $c_0$ in Banach spaces. https://arxiv.org/abs/1502.05753

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