2 results
Decomposability of multiparameter car flows
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 66 / Issue 1 / February 2023
- Published online by Cambridge University Press:
- 31 March 2023, pp. 1-22
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Let P be a closed convex cone in
$\mathbb{R}^d$ which is assumed to be spanning 
$\mathbb{R}^d$ and contains no line. In this article, we consider a family of CAR flows over P and study the decomposability of the associated product systems. We establish a necessary and sufficient condition for CAR flow to be decomposable. As a consequence, we show that there are uncountable many CAR flows which are cocycle conjugate to the corresponding CCR flows.
Examples of multiparameter CCR flows with non-trivial index
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 65 / Issue 3 / August 2022
- Published online by Cambridge University Press:
- 27 September 2022, pp. 799-832
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In this paper, we construct uncountably many examples of multiparameter CCR flows, which are not pullbacks of $1$
-parameter CCR flows, with any given index. Moreover, the constructed CCR flows are type I in the sense that the associated product system is the smallest subsystem containing its units.
