Outgoing Cuntz Scattering System for a Coisometric Lifting and Transfer Function

TL;DR

This paper develops an outgoing Cuntz scattering system for coisometric liftings of operator tuples, introducing a transfer function and comparing it with the characteristic function to enhance input-output analysis in operator theory.

Contribution

It introduces a novel outgoing Cuntz scattering system for coisometric liftings and establishes a connection between transfer and characteristic functions.

Findings

Developed an input-output formalism for coisometric liftings.

Defined a transfer function for the scattering system.

Compared transfer and characteristic functions for the lifting.

Abstract

We study a coisometry that intertwines Popescu's presentations of minimal isometric dilations of a given operator tuple and of a coisometric lifting of the tuple. Using this we develop an outgoing Cuntz scattering system which gives rise to an input-output formalism. A transfer function is introduced for the system. We also compare the transfer function and the characteristic function for the associated lifting.