Salvato in:
| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2411.10771 |
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Sommario:
- For a bounded linear operator $T$ acting on a reproducing kernel Hilbert space $\mathcal{H}(Ω)$ over some non-empty set $Ω$, the Berezin range and the Berezin radius of $T$ are defined respectively, by $\text{Ber}(T) := \{\langle T\hat{k}_λ,\hat{k}_λ \rangle_{\mathcal{H}} : λ\in Ω\}$ and $\text{ber}(T)$ := $\sup\{|γ|: γ\in \text{Ber}(T)\}$, where $\hat{k}_λ$ is the normalized reproducing kernel for $\mathcal{H}(Ω)$ at $λ\in Ω$. In this paper, we study the convexity of the Berezin range of finite rank operators on the Hardy space and the Bergman space over the unit disc $\mathbb{D}$. We present applications of some scalar inequalities to get some operator inequalities. A characterization of closure of the numerical range of reproducing kernel Hilbert space operator in terms of convex hull its Berezin set is discussed.