Ando dilations and inequalities on noncommutative domains
Abstract
We obtain intertwining dilation theorems for noncommutative regular domains D_f and noncommutative varieties V_J of n-tuples of operators, which generalize Sarason and Sz.-Nagy--Foias commutant lifting theorem for commuting contractions. We present several applications including a new proof for the commutant lifting theorem for pure elements in the domain D_f (resp. variety V_J) as well as a Schur type representation for the unit ball of the Hardy algebra associated with the variety V_J. We provide Ando type dilations and inequalities for bi-domains D_f \times D_g and bi-varieties V_J \times V_I. In particular, we obtain extensions of Ando's results and Agler-McCarthy's inequality for commuting contractions to larger classes of commuting operators.
Keywords
Cite
@article{arxiv.1701.00758,
title = {Ando dilations and inequalities on noncommutative domains},
author = {Gelu Popescu},
journal= {arXiv preprint arXiv:1701.00758},
year = {2017}
}
Comments
21 pages, to appear in Proc. Roy. Soc. Edinburgh Section A: Mathematics. arXiv admin note: substantial text overlap with arXiv:1603.00790