9 citations · 16 across the 10 of their papers we have counts for
4 papers · 1 filter
Dilation Theory for Scaled -Numerical Ranges
Matias Kaunisto, Ryan O'Loughlin, Jani Virtanen
We generalise Berger's dilation theorem from numerical ranges to scaled -numerical ranges. Specifically, we prove that if the scaled -numerical range is co…
On the abstract approach to spectral constants: a proof of the Clouâtre--Ostermann--Ransford conjecture
Catalin Badea, Ryan O'Loughlin, Jani Virtanen
Clouâtre, Ostermann, and Ransford formulated an abstract version of Crouzeix's conjecture involving a bounded unital homomorphism from a uniform algebra into matrices and a unital…
Semialgebraic Dimension and Truncated Toeplitz Models for Complex Symmetric Matrices
Ryan O'Loughlin
We answer negatively a finite-dimensional unitary-model question for complex symmetric operators. More precisely, we show that, for every \(n\geq 10\), not every \(n\times n\) symm…
A Counterexample to the Gau--Wang--Wu Conjecture on Partial Isometries
Ryan O'Loughlin, Jani Virtanen
We disprove the conjecture of Gau, Wang and Wu that the numerical range of a finite-dimensional partial isometry, when circular, must be centred at the origin. More precisely, we p…