Browse by author
Lookup NU author(s): Professor Nicholas Young
This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).
We prove a noncommutative analogue of the fact that every symmetric analytic function of $(z,w)$ in the bidisc $\mathbb{D}^2$ can be expressed as an analytic function of the variables $z+w$ and $zw$. We construct an analytic nc-map $S$ from the biball to an infinite-dimensional nc-domain $\Omega$ with the property that, for every bounded symmetric function $\varphi$ of two noncommuting variables that is analytic on the biball, there exists a bounded analytic nc-function $\Phi$ on $\Omega$ such that $\varphi=\Phi\circ S$. We also establish a realization formula for $\Phi$, and hence for $\varphi$, in terms of operators on Hilbert space.
Author(s): Agler J, Young NJ
Publication type: Article
Publication status: Published
Journal: Journal of Functional Analysis
Year: 2014
Volume: 266
Issue: 9
Pages: 5709-5732
Print publication date: 01/05/2014
Online publication date: 11/03/2014
Acceptance date: 19/02/2014
Date deposited: 01/05/2014
ISSN (print): 0022-1236
ISSN (electronic): 1096-0783
Publisher: Academic Press
URL: http://dx.doi.org/10.1016/j.jfa.2014.02.026
DOI: 10.1016/j.jfa.2014.02.026
Notes: Freely available at http://uk.arxiv.org/abs/1307.1588
Altmetrics provided by Altmetric