2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121938We 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 appearOperator AlgebrasFunctional Analysistext