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    Statements

    1984
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    modular automorphism groups of Tomita-Takesaki theory
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    classify Type III factors
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    crossed products of Type II algebras
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    classify the approximately finite-dimensional factors of type \(III_{\lambda }\)
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    uniqueness of injective factors of type \(II_{\infty }\)
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    non-commutative theory of integration
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    non-commutative differential geometry
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