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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Every sum system is divisible


Author: Masaki Izumi
Journal: Trans. Amer. Math. Soc. 361 (2009), 4247-4267
MSC (2000): Primary 46L55, 47D03, 81S05
Published electronically: March 13, 2009
MathSciNet review: 2500888
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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.


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Additional Information

Masaki Izumi
Affiliation: Department of Mathematics, Kyoto University, Kyoto, Japan
Email: izumi@math.kyoto-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04697-2
PII: S 0002-9947(09)04697-2
Keywords: $E_0$-semigroups, product system, type I, type III
Received by editor(s): August 14, 2007
Published electronically: March 13, 2009
Additional Notes: This work was supported by JSPS
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.