On the convergence of sequences of weighted composition operators on certain weighted Hardy spaces

• Published in: Bollettino della Unione matematica italiana (2008) Vol. 17; no. 1; pp. 135 - 147
• Main Authors: Khani-Robati, Bahram, Mehrangiz, Samira
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.03.2024; Springer Nature B.V
• Subjects: Composition; Convergence; Mathematics; Mathematics and Statistics; Operators; Topology; Weak operator convergence; Weighted Bergman spaces; 47B02; Weighted Hardy spaces; Uniform operator convergence; Hilbert Schmidt norm; Primary 47B33; Strong operator convergence; Secondary 47B38; Weighted composition operators
• ISSN: 1972-6724; 2198-2759
• DOI: 10.1007/s40574-023-00388-2

Let H 2 ( β ) be a weighted Hardy space. In this paper under certain conditions on H 2 ( β ) , convergence of a sequence of weighted composition operators in the weak, strong and uniform operator topologies, in terms of the convergence of the corresponding sequences of inducing maps are investigated. Let C ψ , φ be a bounded weighted composition operator and { C ψ , φ n } be the sequence of its powers. Under certain conditions on H 2 ( β ) , φ and ψ we investigate convergence of the induced weighted composition operators C ψ , φ n . Let A G 2 be a weighted Bergman space. In this paper we investigate convergence of a sequence of weighted composition operators in the Hilbert Schmidt norm in terms of the convergence of the corresponding sequences of inducing maps.