Translator Disclaimer
Winter 2018 Completely positive contractive maps and partial isometries
Berndt Brenken
Adv. Oper. Theory 3(1): 271-294 (Winter 2018). DOI: 10.22034/aot.1703-1131

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.

Citation

Download Citation

Berndt Brenken. "Completely positive contractive maps and partial isometries." Adv. Oper. Theory 3 (1) 271 - 294, Winter 2018. https://doi.org/10.22034/aot.1703-1131

Information

Received: 1 March 2017; Published: Winter 2018
First available in Project Euclid: 5 December 2017

zbMATH: 06804326
MathSciNet: MR3730349
Digital Object Identifier: 10.22034/aot.1703-1131

Subjects:
Primary: 46L05, 46L08
Secondary: 46L55

Rights: Copyright © 2018 Tusi Mathematical Research Group

JOURNAL ARTICLE
24 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.3 • No. 1 • Winter 2018
Back to Top