Robustness of Strong Stability of Discrete Semigroups

TL;DR

This paper investigates how the strong stability of discrete semigroups on Hilbert spaces is affected by bounded finite rank perturbations, providing characterizations of perturbations that preserve stability.

Contribution

It offers a characterization of classes of bounded finite rank perturbations that maintain the strong stability of discrete semigroups.

Findings

Identifies classes of perturbations preserving strong stability

Provides a theoretical framework for robustness analysis

Enhances understanding of stability under perturbations

Abstract

In this paper we study the robustness of strong stability of a discrete semigroup on a Hilbert space under bounded finite rank perturbations. As the main result we characterize classes of perturbations preserving the strong stability of the semigroup.