Advances in Operator Theory
- Adv. Oper. Theory
- Volume 3, Number 1 (2018), 271-294.
Completely positive contractive maps and partial isometries
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.
Adv. Oper. Theory, Volume 3, Number 1 (2018), 271-294.
Received: 1 March 2017
First available in Project Euclid: 5 December 2017
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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