Is it possible to explicitly construct the Hilbert space $H$ and operator $T \in B(H)$ such that the von Neumann it generates is type $III$ factor? I would like to see an example.
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5$\begingroup$ Have you tried working through the argument in ams.org/journals/bull/1969-75-01/S0002-9904-1969-12157-9/… ? $\endgroup$– Yemon ChoiCommented Oct 19, 2017 at 0:05
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6$\begingroup$ Olsen and Zame provide an explicit generator of the CAR algebra in ams.org/journals/tran/1976-215-00/S0002-9947-1976-0388114-7/… Then pick a state (Powers '67 Annals) on the CAR algebra that generates a Type III factor. $\endgroup$– Caleb EckhardtCommented Oct 19, 2017 at 0:11
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