Cuntz-Pimsner Algebras, Completely Positive Maps and Morita Equivalence

Details Cuntz-Pimsner Algebras, Completely Positive Maps and Morita Equivalence Cuntz-Pimsner Algebras, Completely Positive Maps and Morita Equivalence

2004-09-27

arxiv.org/abs/math/0409511v1

Mathematics

Operator Algebras

Scientific paper

Let $P$ be a completely positive map on $M_n(\mathbb{C})$ and let $E_P$ be
the associated \emph{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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