Kaydedildi:
| Yazar: | |
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| Materyal Türü: | Preprint |
| Baskı/Yayın Bilgisi: |
2020
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| Konular: | |
| Online Erişim: | https://arxiv.org/abs/2002.07288 |
| Etiketler: |
Etiketle
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| _version_ | 1866908425555804160 |
|---|---|
| author | Severiano, Osmar R. |
| author_facet | Severiano, Osmar R. |
| contents | In this article, we study the complex symmetry of compositions operators $C_ϕf=f\circ ϕ$ induced on weighted Bergman spaces $A^2_β(\mathbb{D}),\ β\geq -1,$ by analytic self-maps of the unit disk. One of ours main results shows that $ϕ$ has a fixed point in $\mathbb{D}$ whenever $C_ϕ$ is complex symmetric. Our works establishes a strong relation between complex symmetry and cyclicity. By assuming $β\in \mathbb{N}$ and $ϕ$ is an elliptic automorphism of $\mathbb{D}$ which not a rotation, we show that $C_ϕ$ is not complex symmetric whenever $ϕ$ has order greater than $2(3+β).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_07288 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Complex symmetry of composition operators on weighted Bergman spaces Severiano, Osmar R. Functional Analysis In this article, we study the complex symmetry of compositions operators $C_ϕf=f\circ ϕ$ induced on weighted Bergman spaces $A^2_β(\mathbb{D}),\ β\geq -1,$ by analytic self-maps of the unit disk. One of ours main results shows that $ϕ$ has a fixed point in $\mathbb{D}$ whenever $C_ϕ$ is complex symmetric. Our works establishes a strong relation between complex symmetry and cyclicity. By assuming $β\in \mathbb{N}$ and $ϕ$ is an elliptic automorphism of $\mathbb{D}$ which not a rotation, we show that $C_ϕ$ is not complex symmetric whenever $ϕ$ has order greater than $2(3+β).$ |
| title | Complex symmetry of composition operators on weighted Bergman spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2002.07288 |