Proximity to ${\ell }_p$ and $c_0$ in Banach spaces

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 $X/Y$.

References in corpus (1)

• Arbitrarily distortable Banach spaces of higher order