Separation Between the Ordinary and Strong Kreiss Constants
Question 6.1 of Chalmoukis, Tsikalas and Yakubovich asks how far the strong Kreiss constant of a matrix can exceed its ordinary Kreiss constant. Answered: for every there are matrices whose Cayley transforms satisfy while with . Since the Kreiss matrix theorem gives in dimension , the exponent is optimal up to an arbitrarily small power loss.
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Construction
- Field
- Operator theory
- Posed by
- Nikolaos Chalmoukis, Georgios Tsikalas and Dmitry Yakubovich
- Year posed
- 2025
- Years open
- 1y
- Solved
- 2026-08-19
- Model
- ChatGPT 5.6 Pro
- Vendor
- OpenAI
- Collaborators
- Emiel Lorist, Martin Meyries, Mark Veraar
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 12 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The same disclosure as the inverse generator entry, since both fall to one paper: ChatGPT 5.6 Pro explored Schauder basis counterexamples, assisted the adaptation of Ansorena's work that produces the explicit basis in Proposition 2.1, and helped optimize the explicit constants. Note the boundary honestly - the disclosure names Proposition 2.1 and Theorem 1.1, not Theorem 1.4. Proposition 2.1 is the finite-dimensional construction every result in the paper is deduced from, including this one, so the model is in the loop for the machinery rather than for this theorem's derivation.
Verification
Checked by this site on 22 August 2026 against the v2 PDF (arXiv:2608.06272v2, 19 Aug): the paper states "We furthermore note that Theorem 1.4(i) solves [6, Question 6.1]" and gives the explicit constants quoted in the statement, and reference [6] is Chalmoukis, Tsikalas and Yakubovich, arXiv:2512.10025. The mathematics of Theorem 1.4 was not checked here, though a curator numerical check of Proposition 2.1 - the construction it is deduced from - was carried out for the sibling entry and confirmed its bounds up to n = 256.
Sources
Related entries
- Same work resolves bothInverse generator problem