Morita equivalence of C*-correspondences passes to the related operator algebras

Abstract

We revisit a central result of Muhly and Solel on operator algebras of C*-correspondences. We prove that (possibly non-injective) strongly Morita equivalent C*-correspondences have strongly Morita equivalent relative Cuntz-Pimsner C*-algebras. The same holds for strong Morita equivalence (in the sense of Blecher, Muhly and Paulsen) and strong $\Delta$-equivalence (in the sense of Eleftherakis) for the related tensor algebras. In particular, we obtain stable isomorphism of the operator algebras when the equivalence is given by a $\sigma$-TRO. As an application we show that strong Morita equivalence coincides with strong $\Delta$-equivalence for tensor algebras of aperiodic C*-correspondences.

20 pages, minor corrections, additional comments in subsection 2.4

References in corpus (3)

• Adding tails to C*-correspondences
• Representations of C*-dynamical systems implemented by Cuntz families
• Stable isomorphism and strong Morita equivalence of operator algebras

Cited by in corpus (1)

• State splitting, strong shift equivalence and stable isomorphism of Cuntz-Krieger algebras