Stinespring's construction as an adjunction

@article{Parzygnat2018StinespringsCA,
  title={Stinespring's construction as an adjunction},
  author={Arthur J. Parzygnat},
  journal={arXiv: Operator Algebras},
  year={2018}
}
Given a representation of a unital $C^*$-algebra $\mathcal{A}$ on a Hilbert space $\mathcal{H}$, together with a bounded linear map $V:\mathcal{K}\to\mathcal{H}$ from some other Hilbert space, one obtains a completely positive map on $\mathcal{A}$ via restriction using the adjoint action associated to $V$. We show this restriction forms a natural transformation from a functor of $C^*$-algebra representations to a functor of completely positive maps. We exhibit Stinespring's construction as a… Expand
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