Contributions to the theory of $\mathrm {C}^*$-correspondences with applications to multivariable dynamics
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- by Evgenios T. A. Kakariadis and Elias G. Katsoulis PDF
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Abstract:
Motivated by the theory of tensor algebras and multivariable $\mathrm {C}^*$-dynamics, we revisit two fundamental techniques in the theory of $\mathrm {C}^*$-corres- pondences, the “addition of a tail” to a non-injective $\mathrm {C}^*$-correspondence and the dilation of an injective $\mathrm {C}^*$-correspondence to an essential Hilbert bimodule. We provide a very broad scheme for “adding a tail” to a non-injective $\mathrm {C}^*$-correspondence; our scheme includes the “tail” of Muhly and Tomforde as a special case. We illustrate the diversity and necessity of our tails with several examples from the theory of multivariable $\mathrm {C}^*$-dynamics. We also exhibit a transparent picture for the dilation of an injective $\mathrm {C}^*$-correspondence to an essential Hilbert bimodule. As an application of our constructs, we prove two results in the theory of multivariable dynamics that extend earlier results. We also discuss the impact of our results on the description of the $\mathrm {C}^*$-envelope of a tensor algebra as the Cuntz-Pimsner algebra of the associated $\mathrm {C}^*$-correspondence.References
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Additional Information
- Evgenios T. A. Kakariadis
- Affiliation: Department of Mathematics, University of Athens, 15784 Athens, Greece
- Email: mavro@math.uoa.gr
- Elias G. Katsoulis
- Affiliation: Department of Mathematics, University of Athens, 15784 Athens, Greece
- Address at time of publication: Department of Mathematics, East Carolina University, Greenville, North Carolina 27858
- MR Author ID: 99165
- Email: katsoulise@ecu.edu
- Received by editor(s): April 19, 2011
- Published electronically: July 17, 2012
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 6605-6630
- MSC (2010): Primary 47L55, 47L40, 46L05, 37B20
- DOI: https://doi.org/10.1090/S0002-9947-2012-05627-3
- MathSciNet review: 2958949