Tensor algebras of C*-correspondences and their C*-envelopes

Katsoulis, Elias G.; Kribs, David W.

Tensor algebras of C-correspondences and their C-envelopes

Authors

Description

We show that the $\ca$-envelope of the tensor algebra of an arbitrary $\ca$-correspondence $\X$ coincides with the Cuntz-Pimsner algebra $Ø_{\X}$, as defined by Katsura \cite{Ka}. This improves earlier results of Muhly and Solel and Fowler, Muhly and Raeburn, who came to the same conclusion under the additional hypothesis that $\X$ is strict and faithful.
9 pages, final version, Journal of Functional Analysis, to appear