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  "conclusion": "The model predicate consists of all three clauses: e is injective; every represented e(a) is compact; and each compact bounded operator T on H equals e(a) for some a in A.",
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  "name": "MathlibAnnex.Analysis.CStarAlgebra.IsCompactOperatorModel",
  "natural_language_statement": "Let A be a complex C*-algebra, not assumed unital, H a complex Hilbert space, and e a nonunital complex star-algebra homomorphism from A to the bounded operators on H. The model predicate consists of all three clauses: e is injective; every represented e(a) is compact; and each compact bounded operator T on H equals e(a) for some a in A.",
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      "text": "IsCompactOperatorModel e ↔ Injective e ∧ (∀ a, IsCompactOperator (e a)) ∧ ∀ T, IsCompactOperator T → ∃ a, e a = T."
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      "text": "This is a definition of a property. It characterizes equality of the image with K(H) together with injectivity; no bundled StarAlgEquiv value is constructed by the definition."
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    "text": "def IsCompactOperatorModel [NonUnitalCStarAlgebra A]\n    (e : A →⋆ₙₐ[ℂ] (H →L[ℂ] H)) : Prop"
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