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Operators commuting with the Volterra operator are not weakly supercyclic

2009/03/10 by Stanislav Shkarin, Shkarin, Stanislav
Mathematics · #37A25 #47A16 #Differential Equations and Boundary Problems #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #math.DS #math.FA #msc:37A25 #msc:47A16

paper · pdf · doi:10.48550/arxiv.0903.1752

Submitted to LMS

arxiv created 2009/03/10 · openalex publication_date 2009/03/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that any bounded linear operator on Lp[0,1] for 1≤ p<∞, commuting with the Volterra operator V, is not weakly supercyclic, which answers affirmatively a question raised by Léon-Saavedra and Piqueras-Lerena. It is achieved by providing an algebraic flavored condition on an operator which prevents it from being weakly supercyclic and is satisfied for any operator commuting with V.

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