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Ideas that do not seem to work · Question 6.1

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

Given ff with ∥f∥∞,W(A)=1\|f\|_{\infty,W(A)}=1, can we always find f~\tilde{f} defined on a ball DD enclosing W(A)W(A) such that f~≈f\tilde{f}\approx f on W(A)W(A) and ∥f~∥∞,D=1\|\tilde{f}\|_{\infty,D}=1?

Lean 4

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Background

Section context

It may be good to have a list of tries that do not seem to succeed.

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.

Status note in the source

Ideally, f~=fϕ\tilde{f}=f\phi for some function phiphi that is approximately equal to 11 on W(A)W(A) and well-behaving outside. If the above was true, then the conjecture should be clear.

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.

Recorded progress

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Discussion

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