Year: 2023
Type: preprint
Abstract: 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 $W_{g,ψ}$ commuting with complex symmetric weighted composition operators $W_{f,φ}$ on the Hardy space $H^2(\mathbb{D})$. In particular, we give the descriptions of the symbols $g$ and $ψ$ such that the inducing weighted composition operator $W_{g,ψ}$ commutes with the complex symmetric weighted composition operator $W_{f,φ}$ with the conjugation $\mathcal{J}$. 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 $φ$.
Source: arXiv (Cornell University)
Author: Bhuia, Sudip Ranjan
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4387687796