Ando dilations and inequalities on noncommutative domains

2017/01/03 by Popescu, Gelu · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1701.00758

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 × D_g and bi-varieties V_J × 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.

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