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Wold decomposition on odometer semigroups

Part of: General theory of linear operators Groups and semigroups of linear operators, their generalizations and applications

Published online by Cambridge University Press:  13 July 2021

Boyu Li Open the ORCID record for Boyu Li [Opens in a new window]
Boyu Li*
Affiliation:
Department of Mathematics and Statistics, University of Victoria, Victoria, B.C., Canada boyuli@uvic.ca
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Abstract

We establish a Wold-type decomposition for isometric and isometric Nica-covariant representations of the odometer semigroup. These generalize the Wold-type decomposition for commuting pairs of isometries due to Popovici and for pairs of doubly commuting isometries due to Słociński.

Keywords

Wold decompositionodometer semigroup

MSC classification

Primary: 47A13: Several-variable operator theory (spectral, Fredholm, etc.)
Secondary: 47A45: Canonical models for contractions and nonselfadjoint operators 47D03: Groups and semigroups of linear operators
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 152 , Issue 3 , June 2022 , pp. 738 - 755
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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