---
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.'
address:
- |
    Department of Mathematics\
    Faculty of Sciences\
    University of Patras\
    26504 Patras\
    Greece
- |
    School of Mathematics and Statistics\
    Newcastle University\
    Newcastle upon Tyne\
    NE1 7RU\
    UK
- |
    Department of Mathematics\
    East Carolina University\
    Greenville, NC 27858\
    USA
author:
- 'George K. Eleftherakis'
- 'Evgenios T.A. Kakariadis'
- 'Elias G. Katsoulis'
title: 'Morita equivalence of C\*-correspondences passes to the related operator algebras'
---

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Introduction
============

Introduced by Rieffel in the 1970’s [@Rie74; @Rie74-2], Morita theory provides an important equivalence relation between C\*-algebras. In the past 25 years there have been fruitful extensions to cover more general (possibly 