Morita Transforms of Tensor Algebras

Details Morita Transforms of Tensor Algebras Morita Transforms of Tensor Algebras

2010-07-20

arxiv.org/abs/1007.3486v1

Mathematics

Operator Algebras

Scientific paper

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 of Hilbert modules over the tensor algebras of $\mathcal{T}_{+}(E)$ and $\mathcal{T}_{+}(F)$. We show that this functor maps absolutely continuous Hilbert modules to absolutely continuous Hilbert modules and provides a new interpretation of Popescu's reconstruction operator.

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