Ryan O’Loughlin

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20242026

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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 $…

Sharp spectral constants for scaled q-numerical ranges

q-Numerical Ranges and Spectral Sets

Sharp spectral constants for scaled $q$ -numerical ranges

$q$ -Numerical Ranges and Spectral Sets