8 papers · 1 filter
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…
Symmetric and Antisymmetric Tensor Products for the Function-Theoretic Operator Theorist
Stephan Ramon Garcia, Ryan O'Loughlin, Jiahui Yu
We study symmetric and antisymmetric tensor products of Hilbert-space operators, focusing on norms and spectra for some well-known classes favored by function-theoretic operator th…
Crouzeix's conjecture for classes of matrices
Ryan O'Loughlin, Jani Virtanen
For a matrix which satisfies Crouzeix's conjecture, we construct several classes of matrices from for which the conjecture will also hold. We discover a new link between cy…
Dual-band general Toeplitz operators
M. Cristina Câmara, Ryan O'Loughlin, Jonathan R. Partington
We relate dual-band general Toeplitz operators to block truncated Toeplitz operators and, via equivalence after extension, with Toeplitz operators with matrix symbols.…