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

Mohammad B. Asadi; Reza Behmani; Ali R. Medghalchi; Hamed Nikpey

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

Operator Algebras 2016-08-16 v2

Authors: Mohammad B. Asadi , Reza Behmani , Ali R. Medghalchi , Hamed Nikpey

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.

Keywords

hilbert modules operator theory on hilbert spaces operator theory

Cite

@article{arxiv.1608.00189,
  title  = {Operator Valued Maps on Hilbert $C^*$-Modules},
  author = {Mohammad B. Asadi and Reza Behmani and Ali R. Medghalchi and Hamed Nikpey},
  journal= {arXiv preprint arXiv:1608.00189},
  year   = {2016}
}

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