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

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

2005-06-08

arxiv.org/abs/math/0506151v4

Journal of Functional Analysis 234 (2006) 226-233

Mathematics

Operator Algebras

9 pages, final version, Journal of Functional Analysis, to appear

Scientific paper

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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