Brian Lins

activity

20152017

collaborators

3 papers

math.FA2017

The normalized numerical range and the Davis-Wielandt shell

Brian Lins, Ilya M. Spitkovsky, Siyu Zhong

For a given $n$ -by- $n$ matrix $A$ , its {\em normalized numerical range} $F_{N} (A)$ is defined as the range of the function $f_{N,A}\colon x\mapsto (x^*Ax)/(\norm{Ax}\cdot\norm{x})$ o…

math.FA2016

Detecting fixed points of nonexpansive maps by illuminating the unit ball

Bas Lemmens, Brian Lins, Roger Nussbaum

We give necessary and sufficient conditions for a nonexpansive map on a finite dimensional normed space to have a nonempty, bounded set of fixed points. Among other results we show…

math.FA2015

Continuous Selections of the Inverse Numerical Range Map

Brian Lins, Parth Parihar

For a complex $n$ -by- $n$ matrix $A$ , the numerical range $F (A)$ is the range of the map $f_{A} (x) = x^{*} A x$ acting on the unit sphere in $\C^n$. We ask whether the multivalued invers…