Cuntz-Pimnser algebras, completely positive maps and Morita equivalence

Marrero, Alberto; Muhly, Paul

doi:10.1090/S0002-9939-05-08110-4

Cuntz-Pimnser algebras, completely positive maps and Morita equivalence
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by Alberto E. Marrero and Paul S. Muhly PDF

Proc. Amer. Math. Soc. 134 (2006), 1133-1135 Request permission

Abstract:

Let $P$ be a completely positive map on $M_n(\mathbb {C})$ and let $E_P$ be the associated GNS-$C^*$-correspondence. We prove a result that implies, in particular, that the Cuntz-Pimsner algebra of $E_P$, $\mathcal {O}(E_P)$, is strongly Morita equivalent to the Cuntz algebra $\mathcal {O}_{d(P)}$, where $d(P)$ is the index of $P$.

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