This is an announcement for the paper "Proximity to $\ell_p$ and $c_0$ in Banach spaces" by Ryan Causey.

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 $X/Y$.

Archive classification: math.FA

Submitted from: CAUSEYRM@mailbox.sc.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1502.05753

or

http://arXiv.org/abs/1502.05753