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

Elias G. Katsoulis, David W. Kribs

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}.…