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Measurable and Continuous Units of an $E_{0}$-semigroup

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  25 March 2020

S. P. Murugan  and
S. Sundar
S. P. Murugan
Affiliation:
Indian Institute of Science, Education and Research, Mohali, 140306, Punjab, India Email: spmath000@gmail.com
S. Sundar
Affiliation:
Institute of Mathematical Sciences (HBNI), Taramani, 600113, Tamilnadu, India Email: sundarsobers@gmail.com
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Abstract

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Let $P$ be a closed convex cone in $\mathbb{R}^{d}$ which is spanning, i.e., $P-P=\mathbb{R}^{d}$ and pointed, i.e., $P\,\cap -P=\{0\}$. Let $\unicode[STIX]{x1D6FC}:=\{{\unicode[STIX]{x1D6FC}_{x}\}}_{x\in P}$ be an $E_{0}$-semigroup over $P$ and let $E$ be the product system associated to $\unicode[STIX]{x1D6FC}$. We show that there exists a bijective correspondence between the units of $\unicode[STIX]{x1D6FC}$ and the units of $E$.

Keywords

E0 -semigroupproduct system unit

MSC classification

Primary: 46L55: Noncommutative dynamical systems
Secondary: 46L99: None of the above, but in this section
Type
Article
Information
Canadian Mathematical Bulletin , Volume 63 , Issue 2 , June 2020 , pp. 469 - 478
Copyright
© Canadian Mathematical Society 2019

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