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  "assumptions": "Let A be a complex C*-algebra, not assumed unital, and form its minimal unitization Unitization ℂ A.",
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  "conclusion": "The infinity character is the character induced by projection onto the scalar coordinate: it evaluates a unitization element at its ℂ component. It is a character of Unitization ℂ A, not of A itself.",
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  "definition_equation": "infinityCharacter = CharacterSpace.equivAlgHom.symm (Unitization.fstHom ℂ A); infinityCharacter(c,a)=c.",
  "definition_explanation": "infinityCharacter = CharacterSpace.equivAlgHom.symm (Unitization.fstHom ℂ A); infinityCharacter(c,a)=c.",
  "display_title": "Scalar character of the minimal unitization",
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  "name": "MathlibAnnex.Analysis.CStarAlgebra.NonUnitalCStarRepresentation.infinityCharacter",
  "natural_language_statement": "Let A be a complex C*-algebra, not assumed unital, and form its minimal unitization Unitization ℂ A. The infinity character is the character induced by projection onto the scalar coordinate: it evaluates a unitization element at its ℂ component. It is a character of Unitization ℂ A, not of A itself.",
  "one_sentence_role": "Defines the distinguished scalar-coordinate character of the minimal unitization.",
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      "text": "Exact Lean statement: {A : Type u} → [inst : NonUnitalCStarAlgebra A] → ↑(WeakDual.characterSpace ℂ (Unitization ℂ A))"
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      "text": "infinityCharacter = CharacterSpace.equivAlgHom.symm (Unitization.fstHom ℂ A); infinityCharacter(c,a)=c."
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    {
      "step_id": "source_route",
      "text": "This is a definition by the scalar-coordinate algebra homomorphism. The later infinityCharacterOn D is its restriction to a chosen star subalgebra D of the unitization."
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  "proof_summary": "This is a definition by the scalar-coordinate algebra homomorphism. The later infinityCharacterOn D is its restriction to a chosen star subalgebra D of the unitization.",
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    "text": "noncomputable def infinityCharacter :\n    WeakDual.characterSpace ℂ (Unitization ℂ A)"
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