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arXiv · 1608.00189

Operator Valued Maps on Hilbert $C^*$-Modules

Mohammad B. Asadi·Reza Behmani·Ali R. Medghalchi·Hamed Nikpey
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Abstract

We provide a characterization for operator valued completely bounded linear maps on Hilbert $C^*$-modules in terms of $\varphi$-maps. Also, we show that for every operator valued completely positive map $\varphi$ on a $C^*$-algebra $\mathcal{A}$, there is a unique (up to multiplication by a unitary operator) non-degenerate $\varphi$-map on each Hilbert $\mathcal{A}$-module.

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Mohammad B. Asadi, Reza Behmani, Ali R. Medghalchi, Hamed Nikpey. 2016-07-31. Operator Valued Maps on Hilbert $C^*$-Modules. https://arxiv.org/abs/1608.00189

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