Operators associated with the hexablock

TL;DR

This paper investigates operator tuples related to the hexablock domain, characterizing their unitaries and isometries, and establishing dilation results, connecting with symmetrized bidisc and tetrablock theories.

Contribution

It provides a characterization of unitaries and isometries for hexablock-contractions and introduces dilation results, linking this domain to other well-studied operator domains.

Findings

Characterization of unitaries and isometries for $ ext{H}$-contractions.

Two types of dilation results for $ ext{H}$-contractions.

Connections established with symmetrized bidisc and tetrablock operators.

Abstract

The hexablock is a domain arising from a special case of the $\mu$-synthesis problem. We study the commuting operator tuples having the hexablock as a spectral set. Such a tuple is called a hexablock-contraction or simply $\mathbb H$-contraction. We characterize the unitaries and isometries associated with $\mathbb H$-contractions. Two different types of dilation results for $\mathbb H$-contractions are obtained. We find connection of this theory with the operators associated with the symmetrized bidisc and tetrablock, two other domains related to the $\mu$-synthesis problem.