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    1987
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    existence of a faithful semi-finite normal trace
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    global innerness of the modular automorphism group
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    Tomita-Takesaki theory
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    Arveson's spectral theory
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    strongly continuous one parameter unitary group
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    direct sum of a semi-finite von Neumann algebra and a purely infinite von Neumann algebra
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    type III property
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    projection lattice
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    global outerness of the modular automorphism group
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