## 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.

Original language | English |
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Pages (from-to) | 3507-3549 |

Number of pages | 43 |

Journal | Transactions of the American Mathematical Society |

Volume | 370 |

Issue number | 5 |

DOIs | |

State | Published - May 2018 |

Externally published | Yes |

### Bibliographical note

Funding Information:Received by the editors July 29, 2015, and, in revised form, August 11, 2016. 2010 Mathematics Subject Classification. Primary 47L30, 46K50, 46H20; Secondary 46L08, 37A30. Key words and phrases. Tensor algebra, weighted partial system, Markov operators, C∗-correspondence, non-deterministic dynamics, classification of non-self-adjoint operator algebras. The author was partially supported by an Ontario Trillium Scholarship.

Publisher Copyright:

© 2018 American Mathematical Society.

## Keywords

- C -correspondence
- Classification of non-self-adjoint operator algebras
- Markov operators
- Non-deterministic dynamics
- Tensor algebra
- Weighted partial system

## ASJC Scopus subject areas

- Mathematics (all)
- Applied Mathematics