Dynamical Systems under Aluthge transforms

TL;DR

This paper demonstrates that certain stability and hyperbolic properties of bounded linear operators on Hilbert spaces are maintained when applying the Aluthge transform, highlighting its preservation of key dynamical features.

Contribution

It establishes that the bounded shadowing property and quasi-hyperbolicity are invariant under the Aluthge transform for bounded linear operators.

Findings

Bounded shadowing property is preserved under Aluthge transforms.

Quasi-hyperbolicity remains intact after applying Aluthge transform.

Aluthge transform maintains key dynamical properties of operators.

Abstract

In this note, we verify that the bounded shadowing property and quasi-hyperbolicity of bounded linear operators on Hilbert spaces are preserved under Aluthge transforms.