Tensor algebras over \(C^*\)-correspondences: Representations, dilations, and \(C^*\)-envelopes
The tensor algebra associated to a \(C^*\)-correspondence (or Hilbert \(C^*\)-module) is a non-commutative generalization of the disk algebra. The main result of this work is that for certain \(C^*\)-correspondences the \(C^*\)-envelope of the tensor algebra is the Cuntz-Pimsner algebra of the correspondence. Along the way results on the existence and structure of dilations, coisometric extensions and commutant lifting are obtained.
tensor algebra associated to a \(C^*\)-correspondence
non-commutative generalization of the disk algebra
scientific article; zbMATH DE number 1215586
scientific article