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

We show that the $\text{ca}$-envelope of the tensor algebra of an arbitrary $\text{ca}$-correspondence $\text{X}$ coincides with the Cuntz-Pimsner algebra ${\text{O}}_{\text{X}}$, 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 $\text{X}$ is strict and faithful.