Strong Morita equivalence for completely positive linear maps on $C^*$-algebras

DOI10.1007/S41980-022-00724-WarXiv2102.13317MaRDI QIDQ6361598

Publication date: 26 February 2021

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.

Mathematics Subject Classification ID

Operator spaces and completely bounded maps (46L07) General theory of (C^*)-algebras (46L05)

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