Rational dilation for operators associated with spectral interpolation and distinguished varieties

TL;DR

This paper characterizes operators linked to the symmetrized polydisc that admit rational dilations and explores their relationship with distinguished varieties within this domain.

Contribution

It provides a characterization of a class of operators associated with the symmetrized polydisc that admit rational dilations and examines their connection with distinguished varieties.

Findings

Operators associated with the symmetrized polydisc admit rational dilations.

A relationship between rational dilation and distinguished varieties is established.

The work advances understanding of spectral interpolation in complex domains.

Abstract

The main aims of this article are to characterize a class of operators associated with the symmetrized polydisc that admit rational dilations on the minimal space and to show an interplay between rational dilation and distinguished varieties in the symmetrized polydisc.