Sudeshna Lahiri | Searcharxiv

arXiv2026

Numerical range and invariant subspaces of weighted composition operators on the Hardy space of Dirichlet series

In this paper, we study various results on numerical range of weighted composition operators on Hardy space of Dirichlet series. Certain conditions are provided under which the numerical range contains zero and some circular or elliptic disks. With the help of invariant subspaces of the operator, we also determine the numerical range of reductive weighted composition operators on this space. Additionally, we discuss some results on the Davis-Wielandt shell of composition operators with some natural questions that arise from our findings.

math.FA↗

arXiv2026

Iterated Aluthge transforms of some composition operators on weighted Bergman spaces

In this paper, we compute the iterated Aluthge transforms $\widetilde{C_ϕ}^{(n)}$ of the composition operator $C_ϕ$ on the weighted Bergman spaces $\mathcal{A}_α^2(\mathbb{D})$, where $ϕ(z)=az+(1-a)$ for $0<a<1$. Also, we obtain the norm and numerical radius of $\widetilde{C_ϕ}^{(n)}$ on $\mathcal{A}_α^2(\mathbb{D})$. We establish that $\widetilde{C_ϕ}^{(n)}$ converges in the strong operator topology on $\mathcal{A}_α^2(\mathbb{D})$. The purpose of this paper is to examine the results of \cite{jung2015iterated} for the weighted Bergman spaces $\mathcal{A}_α^2(\mathbb{D})$. Additionally, by using the iterated Aluthge transforms of $C_ϕ^*$ on $\mathcal{A}_α^2(\mathbb{D})$, we derive the iterated Aluthge transforms of $C_σ$, where $\displaystyleσ(z)=\frac{az}{-(1-a)z+1}$ for $0<a<1$, on some weighted Hardy space $H^2(β_α)$ and study its convergence. Finally, we raise some questions that emerge from these findings.

math.FA↗