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Tensor algebras of C*-correspondences and their C*-envelopes
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Tensor algebras of C*-correspondences and their C*-envelopes
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math.OA
math.FA
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algebramuhlytensoradditionalalgebrasarbitrarycamecite
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We show that the $\ca$-envelope of the tensor algebra of an arbitrary $\ca$-correspondence $\X$ coincides with the Cuntz-Pimsner algebra $\O_{\X}$, 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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