Richard J. Smith

activity

20152019

collaborators

6 papers

math.FA2019

A topological characterization of dual strict convexity in Asplund spaces

Richard J. Smith

Let $X$ be an Asplund space. We show that the existence of an equivalent norm on $X$ having a strictly convex dual norm is equivalent to the dual unit sphere $S_{X^{*}}$ (equivalentl…

math.FA2018

Approximation of norms on Banach spaces

Richard J. Smith, Stanimir Troyanski

Relatively recently it was proved that if $Γ$ is an arbitrary set, then any equivalent norm on $c_{0} (Γ)$ can be approximated uniformly on bounded sets by polyhedral norms and $C^\in…

math.FA2018

Polyhedrality and decomposition

Trond A. Abrahamsen, Vladimir P. Fonf, Richard J. Smith +1

The aim of this note is to present two results that make the task of finding equivalent polyhedral norms on certain Banach spaces, having either a Schauder basis or an uncountable…

math.FA2018

Topology, isomorphic smoothness and polyhedrality in Banach spaces

Richard J. Smith

In recent decades, topology has come to play an increasing role in some geometric aspects of Banach space theory. The class of so-called $w^{*}$ -locally relatively compact sets was i…

stat.ME2017

Improved Density and Distribution Function Estimation

Vitaliy Oryshchenko, Richard J. Smith

Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood pr…

math.FA2015

Smooth and polyhedral approximation in Banach spaces

Victor Bible, Richard J. Smith

We show that norms on certain Banach spaces $X$ can be approximated uniformly, and with arbitrary precision, on bounded subsets of $X$ by $C^{\infty}$ smooth norms and polyhedral n…