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arXiv · 1611.04169

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

George K. Eleftherakis·Evgenios T. A. Kakariadis·Elias G. Katsoulis
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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.

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George K. Eleftherakis, Evgenios T. A. Kakariadis, Elias G. Katsoulis. 2016-11-13. Morita equivalence of C*-correspondences passes to the related operator algebras. https://arxiv.org/abs/1611.04169

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