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Every sum system is divisible
Author(s):
Masaki
Izumi
Journal:
Trans. Amer. Math. Soc.
361
(2009),
4247-4267.
MSC (2000):
Primary 46L55, 47D03, 81S05
Posted:
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:
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
Posted:
March 13, 2009
Additional Notes:
This work was supported by JSPS
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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