Brenken, B. (2018). Completely positive contractive maps and partial isometries. Advances in Operator Theory, 3(1), 271-294. doi: 10.22034/aot.1703-1131
Berndt Brenken. "Completely positive contractive maps and partial isometries". Advances in Operator Theory, 3, 1, 2018, 271-294. doi: 10.22034/aot.1703-1131
Brenken, B. (2018). 'Completely positive contractive maps and partial isometries', Advances in Operator Theory, 3(1), pp. 271-294. doi: 10.22034/aot.1703-1131
Brenken, B. Completely positive contractive maps and partial isometries. Advances in Operator Theory, 2018; 3(1): 271-294. doi: 10.22034/aot.1703-1131
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.