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Abstract: We show that if $M$ and $N$ are $C^{*}$-algebras and if $E$ resp. $F$ is a$C^{*}$-correspondence over $M$ resp. $N$, then a Morita equivalence between$E,M$ and $F,N$ implements a isometric functor between the categories ofHilbert modules over the tensor algebras of $\mathcal{T} {+}E$ and$\mathcal{T} {+}F$. We show that this functor maps absolutely continuousHilbert modules to absolutely continuous Hilbert modules and provides a newinterpretation of Popescu-s reconstruction operator.



Author: Paul S. Muhly, Baruch Solel

Source: https://arxiv.org/







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