Ryan M. Causey

activity

20142023

most citedArbitrarily distortable Banach spaces of higher order

1 citations · 1 across the 6 of their papers we have counts for

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math.FA2023

Equivalence of block sequences in Schreier spaces and their duals

R. M. Causey, A. Pelczar-Barwacz

We prove that any normalized block sequence in a Schreier space $X_{ξ}$ , of arbitrary order $ξ < ω_{1}$ , admits a subsequence equivalent to a subsequence of the canonical basis of some S…

math.FA2022

Asymptotic smoothness and universality in Banach spaces

Ryan M. Causey, Gilles Lancien

For $1 < p ⩽ \infty$ , we study the complexity and the existence of universal spaces for two classes of separable Banach spaces, denoted $A_{p}$ and $N_{p}$ , and…

math.FA2017

The Szlenk index of $L_{p} (X)$ and $A_{p}$

Ryan M. Causey

Given a Banach space $X$ , a $w^{*}$ -compact subset of $X^{*}$ , and $1 < p < \infty$ , we provide an optimal relationship between the Szlenk index of $K$ and the Szlenk index of an associate…

math.FA2016

A note on the relationship between the Szlenk and $w^{}$ -dentability indices of arbitrary $w^{}$ -compact sets

Ryan M Causey

We prove the optimal estimate between the Szlenk and $w^{*}$ -dentability indices of an arbitrary $w^{*}$ -compact subset of the dual of a Banach space. For a given $w^{*}$ -compact, convex…

math.FA2016

Quantitative Factorization of weakly compact, Rosenthal, and $ξ$ -Banach-Saks operators

Kevin Beanland, Ryan M Causey

We prove quantitative factorization results for several classes of operators, including weakly compact, Rosenthal, and $ξ$ -Banach-Saks operators.

math.FA2014★ 1 cited

Arbitrarily distortable Banach spaces of higher order

Kevin Beanland, Ryan Causey, Pavlos Motakis

We study an ordinal rank on the class of Banach spaces with bases that quantifies the distortion of the norm of a given Banach space. The rank $A D (\cdot)$ , introduced by P. Dodos,…