### Completely positive contractive maps and partial isometries

Berndt Brenken

#### Abstract

Associated with a completely positive contractive map $\varphi$ of a $C^*$-algebra $A$ is a universal $C^*$-algebra generated by the $C^*$-algebra $A$ along with a contraction implementing $\varphi$. We prove a dilation theorem: the map $\varphi$ may be extended to a completely positive contractive map of an augmentation of $A$. The associated $C^*$-algebra of the augmented system contains the original universal $C^*$-algebra as a corner, and the extended completely positive contractive map is implemented by a partial isometry.

#### Article information

Source
Adv. Oper. Theory, Volume 3, Number 1 (2018), 271-294.

Dates
First available in Project Euclid: 5 December 2017

https://projecteuclid.org/euclid.aot/1512497962

Digital Object Identifier
doi:10.22034/aot.1703-1131

Mathematical Reviews number (MathSciNet)
MR3730349

Zentralblatt MATH identifier
06804326

#### Citation

Brenken, Berndt. Completely positive contractive maps and partial isometries. Adv. Oper. Theory 3 (2018), no. 1, 271--294. doi:10.22034/aot.1703-1131. https://projecteuclid.org/euclid.aot/1512497962

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