5 papers
Square Functions, Complete Crouzeix Conjecture in Dimension Three, and the Clouâtre-Ostermann-Ransford conjecture
Per Åhag, Rafał Czyż, Jani Virtanen
We settle the complete Crouzeix conjecture for matrices of order at most three and prove the Q-algebra case of the completely bounded Clouâtre-Ostermann-Ransford (COR) conjecture f…
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…
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…
Maximal Plurisubharmonic Functions and Fujii-Seo Determinants in Hilbert spaces
Per Åhag, Rafał Czyż, Antti Perälä +1
Let be a complex Hilbert space and let be a domain. In infinite dimensions, there is no canonical complex Monge--Ampère operator and no basis-free determinant of t…
A survey of asymptotics of determinants for structured matrices
E. Basor, T. Ehrhardt, J. A. Virtanen
In this survey we show how to produce asymptotics of determinants of structured matrices using operator theory methods. We describe the asymptotics for finite Toeplitz matrices, fi…