Three results in linear dynamics

2023/10/21 by Mohammad Ansari, Ansari, Mohammad
Mathematics · #47A16 (Primary) 46E10 (Secondary) #Advanced Topics in Algebra #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2310.14099

openalex publication_date 2023/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, first we show that the Fréchet space H(\Bbb D) cannot support strongly supercyclic weighted composition operators. Then we compute the constant ε for weighted backward shifts on ℓ^p (1≤ p<∞) and c₀. This constant is used to find strongly hypercyclic scalar multiples of non-invertible strongly supercyclic Banach space operators. Finally, we give an affirmative answer to a recent open question concerning supercyclic vectors.

Related

• Ultra hypercyclicity and its connection to mixing properties
• Supercyclic weighted composition operators on the space of smooth functions
• Weak disjointness of hypercyclic operators
• Dynamics of weighted shifts on ℓ^p-sums and c₀-sums
• Common hypercyclic vectors for multiples of backward shift