Isomorphisms of tensor algebras arising from weighted partial systems

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)3507-3549
Number of pages43
JournalTransactions of the American Mathematical Society
Issue number5
StatePublished - May 2018
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2018 American Mathematical Society.


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

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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