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

@article{Katsoulis2005TensorAO,
  title={Tensor algebras of C∗-correspondences and their C∗-envelopes},
  author={E. Katsoulis and D. Kribs},
  journal={Journal of Functional Analysis},
  year={2005},
  volume={234},
  pages={226-233}
}
Abstract We show that the C ∗ -envelope of the tensor algebra of an arbitrary C ∗ -correspondence X coincides with the Cuntz–Pimsner algebra O X , as defined by Katsura [T. Katsura, On C ∗ -algebras associated with C ∗ -correspondences, J. Funct. Anal. 217 (2004) 366–401]. This improves earlier results of Muhly and Solel [P.S. Muhly, B. Solel, Tensor algebras over C ∗ -correspondences: Representations, dilations and C ∗ -envelopes, J. Funct. Anal. 158 (1998) 389–457] and Fowler, Muhly and… Expand
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