Every sum system is divisible

Author:
Masaki Izumi

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

Published electronically:
March 13, 2009

MathSciNet review:
2500888

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-09-04697-2

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.