trureturingGitHub MATHEMATICAL ATLAS

Quantum / CONCEPT

Gazeau's Schwartz action admits no normal Hilbert realization

The ordinary Gazeau block action on the full Schwartz core has no closed densely defined self-adjoint, skew-adjoint, or normal realization under any complete positive Hilbert metric on the fixed complex vector space.

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DIRECT CONSEQUENCES0
PROOF DEPTH1
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THEOREM

All three adjoint alternatives are impossible

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Gaussian Schwartz MapsGaussian Schwartz MapsGazeau's Schwartz action admits no normal Hilbert realizationGazeau's Schwartz action admitsno normal Hilbert realization
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Lean sourceResearch workspace
Status
Closed
Depth
1
Layer
D5/S3
Domain
Quantum
Node ID
D5/S3/Quantum/Analysis/GazeauNormalRealization
Repository path
D5/S3/Quantum/Analysis/GazeauNormalRealization.lean
Truth release
sha256:099187d7dec45101df1543521dfae400188aaa00645a3a61e95e49a3c2be8108
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535a6648df930c3bfdca8a945bfcebdb0d0e1ec7
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b898bd4223ba7e28b9490cfb432638d5338589a1

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Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.