Isometric dilations and von Neumann inequality for finite rank commuting contractions

Sibaprasad Barik, B. Krishna Das, Jaydeb Sarkar

Published 2018-04-16Version 1

It is well known that for an arbitrary $n$-tuple of commuting contractions, $n\geq 3$, neither the existence of isometric dilation nor the von-Neumann inequality holds. In this paper we provide an explicit isometric dilation for a large class of $n$-tuple $(n\geq 3)$ of commuting contractions. The present class of tuples of operators is motivated by a polydisc version of commutant lifting theorem by Ball, Li, Timotin and Trent. The present class of operators is larger than the one considered in \cite{BDHS}. Also we prove a sharper von-Neumann inequality on an algebraic variety in the closure of the polydisc in $\mathbb{C}^n$.