Every sum system is divisible
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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.References
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Additional Information
- Masaki Izumi
- Affiliation: Department of Mathematics, Kyoto University, Kyoto, Japan
- Email: izumi@math.kyoto-u.ac.jp
- Received by editor(s): August 14, 2007
- Published electronically: March 13, 2009
- Additional Notes: This work was supported by JSPS
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 4247-4267
- MSC (2000): Primary 46L55, 47D03, 81S05
- DOI: https://doi.org/10.1090/S0002-9947-09-04697-2
- MathSciNet review: 2500888