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Optimal constant dependence for Ritt-operators · Question 8.2

Crouzeix's conjecture · AIMPL workshop record

MSC 47 · Operator theory

Editorial mapping of AIMPL list topic: Crouzeix's conjecture. http://aimpl.org/crouzeix/ Not an author-supplied MSC code.

Workshop record · status unassessedAs of 2026-09-10 source snapshot; not a current-status certificationSource & evidence ↓
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Problem statement

What is the best constant CC here?

Lean 4

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Background

Section context

A problem that is a bit less connected to Crouzeix's conjecture, but may require similar techniques coming from function theory.

Question context

If we have additionally the spectrum in the open unit disc

∣∣(zI−T)−1∣∣≤M|| (zI-T)^{-1} || \le M for ∣z∣≥1|z| \ge 1.

Then it is known that with C=4C=4 the following holds

∑j=1∞∣∣Tj∣∣≤CM(M−1)\sum_{j=1}^\infty || T^j || \le C M (M-1)

Progress & source assessment

Dated source record, inspected 2026-09-10. Current status has not been independently reassessed. Source-reported results have not been independently verified.

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References
  1. [1]Crouzeix's conjecture · Original question link
  2. [2]AIMPL source bibliography link
  3. [3]AIMPL text license · CC BY-SA 3.0 linkAIM Problem Lists (AIMPL), original contributors; CC BY-SA 3.0. Adaptation: structural TeX converted to Markdown, documented source macros expanded, and source bibliography links added. Mathematical wording retained. These adapted source texts remain under CC BY-SA 3.0.

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