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

Elias G. Katsoulis·David W. Kribs
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Abstract

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.

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Elias G. Katsoulis, David W. Kribs. 2005-12-28. Tensor algebras of C*-correspondences and their C*-envelopes. https://arxiv.org/abs/math/0506151

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