Infinite-operator invariant-subspace fixture

Family 293: Invariant projections, hyperinvariant subspaces, and transitive algebras. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Track nonzero norm-quasinilpotent infinite-Hilbert-space and hyperfinite-factor counterexamples to specified invariant-subspace properties.

Applicability and commercial boundary

Finite-dimensional invariant-subspace intuition does not transfer; hyperinvariant and invariant projection claims must remain separate.

Initial business decision

Research reference or conditional symbolic/verification engineering. No recurring buyer need, practical implementation or profitability has been demonstrated. Defer a standalone commercial product until a constructive example and a measurable workflow improvement exist. These records also identify unsupported inferences that an evidence platform could flag.

Next verification action

Read explicit construction and test only valid finite approximations.

Evidence scope

The repository catalog statement was individually read. Main-paper construction, effectiveness and selected formal-scope comparison remain queued for this record. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.

Invariant-projection counterexamples for every irrational rotation.