Agler-Commutant Lifting on an Annulus

TL;DR

This paper establishes a new commutant lifting theorem for the annulus using minimal inner functions as test functions, with a unique model space characterized by a zero-free reproducing kernel.

Contribution

It introduces a test function style commutant lifting theorem specific to the annulus, utilizing the Sarason Hardy space with a zero-free kernel.

Findings

Proves a commutant lifting theorem for the annulus.

Identifies the Sarason Hardy space as the unique model space.

Uses minimal inner functions as test functions.

Abstract

The main result is a test function style commutant lifting theorem for an annulus A. The test functions are the minimal inner functions for A. The model space is the Sarason Hardy Hilbert space for A uniquely determined by the fact that its reproducing kernel has no zeros.