9 citations · 16 across the 10 of their papers we have counts for
12 papers
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…
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…
Symmetric matrix representations of truncated Toeplitz operators on finite dimensional spaces
Ryan O'Loughlin
In this paper, we study matrix representations of truncated Toeplitz operators with respect to orthonormal bases which are invariant under a canonical conjugation map. In particula…
Symbols of compact truncated Toeplitz operators
Ryan O'Loughlin
This paper characterises the dual of the model space , where is an inner function, intersected with the shifted Hardy space, . With this duality result, it is the…
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.…
Matrix-valued truncated Toeplitz operators: unbounded symbols, kernels and equivalence after extension
Ryan O'Loughlin
This paper studies matrix-valued truncated Toeplitz operators, which are a vectorial generalisation of truncated Toeplitz operators. It is demonstrated that, although there exist m…
Nearly invariant subspaces with applications to truncated Toeplitz operators
Ryan O'Loughlin
In this paper we first study the structure of the scalar and vector-valued nearly invariant subspaces with a finite defect. We then subsequently produce some fruitful applications…
Toeplitz kernels and the backward shift
Ryan O'Loughlin
In this paper we study the kernels of Toeplitz operators on both the scalar and the vector-valued Hardy space for . We show existence of a minimal kernel of any e…