Every sum system is divisible

Izumi, Masaki

doi:10.1090/S0002-9947-09-04697-2

Every sum system is divisible
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Trans. Amer. Math. Soc. 361 (2009), 4247-4267 Request permission

Abstract:

We show that every sum system is divisible. Combined with B. V. R. Bhat and R. Srinivasan’s result, this shows that every product system arising from a sum system (and every generalized CCR flow) is either of type I or type III. A necessary and sufficient condition for such a product system to be of type I is obtained.

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