Generalized multipliers for left-invertible operators and applications

TL;DR

This paper introduces generalized multipliers for left-invertible operators, representing them as analytic functions on an annulus or disc, with potential applications in operator theory.

Contribution

It defines a new class of multipliers for left-invertible operators and explores their representation as analytic functions, expanding the theoretical framework.

Findings

Generalized multipliers are formal Laurent series for left-invertible operators.

These series can be represented as analytic functions on an annulus or disc.

The approach broadens understanding of operator representations in complex analysis.

Abstract

We introduce generalized multipliers for left-invertible operators which formal Laurent series $U_x(z)=\sum_{n=1}^\infty(P_ET^{n}x) \frac{1}{z^n}+\sum_{n=0}^\infty(P_E{T^{\prime*}}^{n}x)z^n$ actually represent analytic functions on an annulus or a disc.