On discrete subordination of power bounded and Ritt operators

TL;DR

This paper advances the understanding of discrete subordination in the functional calculus of power bounded and Ritt operators, introducing a new technique that generalizes previous results and addresses open questions.

Contribution

It develops a new technique for discrete subordination, showing convex combinations of Ritt operators are Ritt, and unifies several main results in the area.

Findings

Convex combinations of Ritt operators are Ritt

Unified framework for discrete subordination results

Answered an open question from prior work

Abstract

By means of a new technique, we develop further a discrete subordination approach to the functional calculus of power bounded and Ritt operators initiated by N. Dungey in [19]. This allows us to show, in particular, that (infinite) convex combinations of powers of Ritt operators are Ritt. Moreover, we provide a unified framework for several main results on discrete subordination from [19] and answer a question left open in [19]. The paper can be considered as a complement to [26] for the discrete setting.