2021/08/04 by Noureddine Karim, Karim, Noureddine, Otmane Benchiheb +3
Mathematics · #46T25 #47B20. Secondarily 46E50 #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions #Primarily 47A16
paper · pdf · doi:10.48550/arxiv.2108.01956
openalex publication_date 2021/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A bounded linear operator T acting on a Hilbert space H is said to be recurrent if for every non-empty open subset U⊂ H there is an integer n such that Tn (U)∩ U≠∅. In this paper, we completely characterize the recurrence of scalar multiples of composition operators, induced by linear fractional self maps of the unit disk, acting on weighted Dirichlet spaces Sν; in particular on the Bergman space, the Hardy space, and the Dirichlet space. Consequently, we complete a previous work of Costakis et al. \citecostakis on recurrence of linear fractional composition operators on Hardy space. In this manner, we determine the triples (λ,ν,ϕ)∈ ℂ× ℝ× LFM(\mathbbD) for which the scalar multiple of composition operator λCϕ acting on Sν fails to be recurrent.