Adding tails to $C^*$-correspondences

By P. Muhly, M. Tomforde. Documenta Mathematica, 2002

77 citations recorded by the source corpus.

We describe a method of adding tails to C*-correspondences which generalizes the process used in the study of graph C*-algebras. We show how this technique can be used to extend results for augmented Cuntz-Pimsner algebras to C*-algebras associated to general C*-correspondences, and as an application we prove a gauge-invariant uniqueness theorem for these algebras. We also define a notion of relative graph C*-algebras and show that properties of these C*-algebras can provide insight and motivation for results about relative Cuntz-Pimsner algebras.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9d025f813ff40f2a5fb9bce595ca96460837d585

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Elias G. Katsoulis
2. David W. Kribs
3. P. Muhly
4. M. Tomforde
5. K. Davidson
6. Gelu Popescu
7. Aidan Sims
8. G. Abrams

In Statistical and Nonlinear Physics

1. Elias G. Katsoulis
2. David W. Kribs
3. M. Tomforde
4. P. Muhly
5. Vern I. Paulsen
6. G. Abrams

Citations in the corpus

• Tensor algebras of C∗-correspondences and their C∗-envelopes (2005, methodology): “” This process has been generalized to arbitrary correspondences by Muhly and Tomforde [12].”
• Topological Quivers (2003, methodology): “We refer the reader to the work of Katsura as well as the introduction of [41] for a more detailed explanation of why O(JX , X) is the appropriate definition for the general Cuntz-Pimsner algebra.”