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Isomorphisms of tensor algebras arising from weighted partial systems

Author: Adam Dor-On
Journal: Trans. Amer. Math. Soc. 370 (2018), 3507-3549
MSC (2010): Primary 47L30, 46K50, 46H20; Secondary 46L08, 37A30
Published electronically: January 18, 2018
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Abstract: We continue the study of isomorphisms of tensor algebras associated to $ C^*$-correspondences in the sense of Muhly and Solel. Inspired by recent work of Davidson, Ramsey, and Shalit, we solve isomorphism problems for tensor algebras arising from weighted partial dynamical systems. We provide complete bounded / isometric classification results for tensor algebras arising from weighted partial systems, both in terms of the $ C^*$-correspondences associated to them and in terms of the original dynamics. We use this to show that the isometric isomorphism and algebraic / bounded isomorphism problems are two distinct problems that require separate criteria to be solved. Our methods yield alternative proofs to classification results for Peters' semi-crossed product due to Davidson and Katsoulis and for multiplicity-free graph tensor algebras due to Katsoulis, Kribs, and Solel.

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Additional Information

Adam Dor-On
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada
Address at time of publication: Department of Mathematics, Technion - Israel institute of Technology, Haifa, 3200003, Israel

Keywords: Tensor algebra, weighted partial system, Markov operators, $C^*$-correspondence, non-deterministic dynamics, classification of non-self-adjoint operator algebras
Received by editor(s): July 29, 2015
Received by editor(s) in revised form: August 11, 2016
Published electronically: January 18, 2018
Additional Notes: The author was partially supported by an Ontario Trillium Scholarship
Article copyright: © Copyright 2018 American Mathematical Society

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