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arXiv · 2505.24495

Convexity of the Berezin range of operators on $\mathcal{H}_\gamma (\mathbb{D})$

Sandip Kumar Maiti·Satyajit Sahoo·Gorachand Chakraborty
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Abstract

In this paper, we characterize the convexity of the Berezin range for finite-rank operators acting on the weighted Hardy space $\mathcal{H}_\gamma (\mathbb{D})$ over the unit disc $\mathbb{D}$. We provide a complete classification in terms of convexity for concrete operators. Additionally, we address dynamical properties of finite-rank operators on Hardy and Bergman spaces. Several illustrative examples are discussed to support our theoretical findings. Additionally, geometrical interpretations have also been employed.

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Sandip Kumar Maiti, Satyajit Sahoo, Gorachand Chakraborty. 2025-05-30. Convexity of the Berezin range of operators on $\mathcal{H}_\gamma (\mathbb{D})$. https://arxiv.org/abs/2505.24495

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