Brian Lins

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20152020

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6 papers · 1 filter

math.FA2020

The essential numerical range and a theorem of Simon on the absorption of eigenvalues

Brian Lins

Let $A (t)$ be a holomorphic family of self-adjoint operators of type (B) on a complex Hilbert space $H$ . Kato-Rellich perturbation theory says that isolated eigenvalues o…

math.FA2020

Numerical ranges encircled by analytic curves

Brian Lins

Let $D$ be a bounded convex domain in $C$ with a regular analytic boundary. Suppose that the numerical range $W (A)$ of a bounded linear operator $A$ is contained in $\over…

math.FA2018

Inverse continuity of the numerical range map for Hilbert space operators

Brian Lins, Ilya Spitkovsky

We describe continuity properties of the multivalued inverse of the numerical range map $f_{A} : x \mapsto ⟨ A x, x ⟩$ associated with a linear operator $A$ defin…

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…