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Decomposability of multiparameter car flows

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  31 March 2023

Anbu Arjunan
Anbu Arjunan*
Affiliation:
Indian Statistical Institute, Delhi Centre, Delhi 110016, India (aanbu100@gmail.com)
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Abstract

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.

Keywords

E0-semigroupsCCR flowsCAR flowsadditive decomposable vectorsquantum stochastic equation

MSC classification

Primary: 46L55: Noncommutative dynamical systems
Secondary: 46L99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 66 , Issue 1 , February 2023 , pp. 1 - 22
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society.

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