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Strong Morita Equivalence for Completely Positive Linear Maps on \(C^*\)-Algebras

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Abstract

We will introduce the notion of strong Morita equivalence for completely positive linear maps and study its basic properties. Also, we will discuss the relation between strong Morita equivalence for bounded \(C^*\)-bimodule linear maps and strong Morita equivalence for completely positive linear maps. Furthermore, we will show that if two unital \(C^*\)-algebras are strongly Morita equivalent, then there is a \(1-1\) correspondence between the two sets of all strong Morita equivalence classes of completely positive linear maps on the two unital \(C^*\)-algebras and we will show that the corresponding two classes of the completely positive linear maps are also strongly Morita equivalent.

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Acknowledgements

The author wishes to thank the referees for many valuable suggestions for improvement of the manuscript.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Faculty of Science, Ryukyu University, Nishihara-cho, Okinawa, 903-0213, Japan

    Kazunori Kodaka

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  1. Kazunori Kodaka
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Correspondence to Kazunori Kodaka.

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Communicated by Mohammad B. Asadi.

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Kodaka, K. Strong Morita Equivalence for Completely Positive Linear Maps on \(C^*\)-Algebras. Bull. Iran. Math. Soc. 48, 3743–3765 (2022). https://doi.org/10.1007/s41980-022-00724-w

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  • DOI: https://doi.org/10.1007/s41980-022-00724-w

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