Crouzeix's conjecture for classes of matrices

O'Loughlin, R. and Virtanen, J. (2023) Crouzeix's conjecture for classes of matrices. Linear Algebra and its Applications. ISSN 0024-3795 doi: 10.1016/j.laa.2023.12.008

Abstract/Summary

For a matrix A which satisfies Crouzeix's conjecture, we construct several classes of matrices from A for which the conjecture will also hold. We discover a new link between cyclicity and Crouzeix's conjecture, which shows that Crouzeix's Conjecture holds in full generality if and only if it holds for the differentiation operator on a class of analytic functions. We pose several open questions, which if proved, will prove Crouzeix's conjecture. We also begin an investigation into Crouzeix's conjecture for symmetric matrices and in the case of matrices, we show Crouzeix's conjecture holds for symmetric matrices if and only if it holds for analytic truncated Toeplitz operators.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/114467
Identification Number/DOI	10.1016/j.laa.2023.12.008
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Elsevier
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