R. Causey

collaborators

6 papers

math.FA2016

$ξ$ -asymptotically uniformly smooth, $ξ$ -asymptotically uniformly convex, and $(β)$ operators

Ryan M. Causey, Stephen J. Dilworth

For each ordinal $ξ$ , we define the notions of $ξ$ -asymptotically uniformly smooth and $w^{*}$ - $ξ$ -asymptotically uniformly convex operators. When $ξ = 0$ , these extend the notions of…

math.FA2016

Szlenk and $w^{*}$ -dentability indices of $C (K)$

Ryan M Causey

Given any compact, Hausdorff space $K$ and $1 < p < \infty$ , we compute the Szlenk and $w^{*}$ -dentability indices of the spaces $C (K)$ and $L_{p} (C (K))$ . We show that if $K$ is compact, H…

math.FA2016

Metrical Characterizations of super weakly compact operators

Ryan M. Causey, Stephen J. Dilworth

We characterize super weakly compact operators as those through which binary tree and diamond and Laakso graphs may not be factored with uniform distortion.

math.FA2016

On a generalization of Bourgain's tree index

Kevin Beanland, Ryan Causey

For a Banach space $X$ , a sequence of Banach spaces $(Y_{n})$ , and a Banach space $Z$ with an unconditional basis, D. Alspach and B. Sari introduced a generalization of a Bourgain tr…

math.FA2015

An alternate description of the Szlenk index with applications

Ryan M. Causey

We discuss an alternate method for computing the Szlenk index of an arbitrary $w^{*}$ compact subset of the dual of a Banach space. We discuss consequences of this method as well as…

math.FA2015

Proximity to $ℓ_{p}$ and $c_{0}$ in Banach spaces

Ryan Causey

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 a…

ξ-asymptotically uniformly smooth, ξ-asymptotically uniformly convex, and (β) operators

Szlenk and w∗-dentability indices of C(K)

Metrical Characterizations of super weakly compact operators

On a generalization of Bourgain's tree index

An alternate description of the Szlenk index with applications

Proximity to ℓp​ and c0​ in Banach spaces

$ξ$ -asymptotically uniformly smooth, $ξ$ -asymptotically uniformly convex, and $(β)$ operators

Szlenk and $w^{*}$ -dentability indices of $C (K)$

Proximity to $ℓ_{p}$ and $c_{0}$ in Banach spaces