Abstract
We investigate the complex symmetric structure of the weighted composition operator $W_{\psi,\phi}$ on the subspace $\mathcal{H}_{\alpha, \beta}^2(\mathbb{D})$ of the Hardy space $\mathcal{H}^2(\mathbb{D})$ of codimension one. We provide characterizations of symbols $\phi$ and $\psi$ such that $W_{\psi,\phi}$ is complex symmetric with respect to a special conjugation. In addition, we discuss isometric properties of the complex symmetric operator $W_{\psi,\phi}$ on $\mathcal{H}_{\alpha, \beta}^2(\mathbb{D})$.
Citation
Aastha Malhotra. Anuradha Gupta. "Complex symmetry of weighted composition operators on the space $\mathcal{H}_{\alpha, \beta}^2(\mathbb{D})$." Bull. Belg. Math. Soc. Simon Stevin 27 (4) 595 - 607, november 2020. https://doi.org/10.36045/j.bbms.200316
Information