Expansivity and strong structural stability for composition operators on L^p spaces

2022/06/01 by Martina Maiuriello, Maiuriello, Martina · 3 citations
Mathematics · #37B65 #37C20 #Advanced Banach Space Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Primary: 47B33 #Secondary: 37B05 #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2206.00353

openalex publication_date 2022/06/01 · openalex created_date 2022/06/13 · openalex updated_date 2026/07/28

Abstract

In this note we investigate the two notions of expansivity and strong structural stability for composition operators on L^p spaces, 1 ≤ p < ∞. Necessary and sufficient conditions for such operators to be expansive are provided, both in the general and the dissipative case. We also show that, in the dissipative setting, the shadowing property implies the strong structural stability and we prove that these two notions are equivalent under the extra hypothesis of positive expansivity.

Cited by

• On the Dynamics of Weighted Composition Operators II
• On Notions of Expansivity for Operators on Locally Convex Spaces
• On the Dynamics of Weighted Composition Operators

Related

• Some classes of composition operators on Orlicz spaces
• On the Dynamics of Weighted Composition Operators II
• Expansivity Property for Composition Operators on Orlicz -Lorentz Spaces
• On Notions of Expansivity for Operators on Locally Convex Spaces
• Shadowing and structural stability in linear dynamical systems