2023/10/13 by Sudip Ranjan Bhuia, Bhuia, Sudip Ranjan
Mathematics · #47A05 #47B20 #47B33 #47B38 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2310.09026
openalex publication_date 2023/10/13 · openalex created_date 2023/10/17 · openalex updated_date 2026/07/28
In this paper, we initially study when an anti-linear Toeplitz operator is in the commutant of a composition operator. Primarily, we investigate weighted composition operators Wg,ψ commuting with complex symmetric weighted composition operators Wf,φ on the Hardy space H2(\mathbbD). In particular, we give the descriptions of the symbols g and ψ such that the inducing weighted composition operator Wg,ψ commutes with the complex symmetric weighted composition operator Wf,φ with the conjugation J. Furthermore, we subsequently demonstrate that these weighted composition operators are normal and complex symmetric in accordance with the properties of the fixed point of the associated symbol φ.