Ryan O’Loughlin

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20242026

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6 papers · 1 filter

math.FA2026

Sharp spectral constants for scaled $q$ -numerical ranges

Mohamed Amine Aouichaoui, Ryan O'Loughlin

For $n \geq 2$ , $A \in M_{n} (C)$ and $0 < ∣ q ∣ \leq 1$ , let $Ω_{q} (A) = q^{- 1} W_{q} (A)$ be the scaled $q$ -numerical range. We prove that for every $γ \geq 1$ , \[ Ω_{η(γ)}(A) =\bigcup_{κ…

math.FA2026

$q$ -Numerical Ranges and Spectral Sets

Ryan O'Loughlin, Jyoti Rani

We study spectral constants for convex domains $Ω$ containing the spectrum of an operator. We extend the Crouzeix--Palencia framework by obtaining bounds depending on a parameter $…

math.FA2025

Describing the Numerical Range and $C$ -Numerical Range of Matrices via Their Unitary Orbits and the Joukowsky Transform

Ryan O'Loughlin

We generalise the Elliptical Range Theorem to characterise the numerical range of matrices belonging to a subspace of the space of $3 \times 3$ matrices. Using Specht's Theorem,…

math.FA2025

Bounded Toeplitz Products on the Hardy Space

Ryan O'Loughlin

A Toeplitz operator on the Hardy space of the unit circle is bounded if and only if its symbol is bounded. For two Toeplitz operators, there are no known function-theoretic conditi…

math.FA2024

On the Crouzeix ratio for $N \times N$ matrices

Bartosz Malman, Javad Mashreghi, Ryan O'Loughlin +1

The Crouzeix ratio $ψ (A)$ of an $N \times N$ complex matrix $A$ is the supremum of $∥ p (A) ∥$ taken over all polynomials $p$ such that $∣ p ∣ \leq 1$ on the numerical range of $A$ . It i…

math.FA2024

Double-layer potentials, configuration constants and applications to numerical ranges

Bartosz Malman, Javad Mashreghi, Ryan O'Loughlin +1

Given a compact convex planar domain $Ω$ with non-empty interior, the classical Neumann's configuration constant $c_{R} (Ω)$ is the norm of the Neumann-Poincaré operator $K…

Sharp spectral constants for scaled q-numerical ranges

q-Numerical Ranges and Spectral Sets

Describing the Numerical Range and C-Numerical Range of Matrices via Their Unitary Orbits and the Joukowsky Transform