Operators commuting with complex symmetric weighted composition operators on $H^2$
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866917738355621888 |
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| author | Bhuia, Sudip Ranjan |
| author_facet | Bhuia, Sudip Ranjan |
| contents | In this paper, we initially study when an anti-linear Toeplitz operator is in the commutant of a composition operator. Primarily, we investigate weighted composition operators $W_{g,ψ}$ commuting with complex symmetric weighted composition operators $W_{f,φ}$ on the Hardy space $H^2(\mathbb{D})$. In particular, we give the descriptions of the symbols $g$ and $ψ$ such that the inducing weighted composition operator $W_{g,ψ}$ commutes with the complex symmetric weighted composition operator $W_{f,φ}$ with the conjugation $\mathcal{J}$. Furthermore, we subsequently demonstrate that these weighted composition operators are normal and complex symmetric in accordance with the properties of the fixed point of the associated symbol $φ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_09026 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Operators commuting with complex symmetric weighted composition operators on $H^2$ Bhuia, Sudip Ranjan Functional Analysis Complex Variables Operator Algebras 47B20, 47A05, 47B38, 47B33 In this paper, we initially study when an anti-linear Toeplitz operator is in the commutant of a composition operator. Primarily, we investigate weighted composition operators $W_{g,ψ}$ commuting with complex symmetric weighted composition operators $W_{f,φ}$ on the Hardy space $H^2(\mathbb{D})$. In particular, we give the descriptions of the symbols $g$ and $ψ$ such that the inducing weighted composition operator $W_{g,ψ}$ commutes with the complex symmetric weighted composition operator $W_{f,φ}$ with the conjugation $\mathcal{J}$. Furthermore, we subsequently demonstrate that these weighted composition operators are normal and complex symmetric in accordance with the properties of the fixed point of the associated symbol $φ$. |
| title | Operators commuting with complex symmetric weighted composition operators on $H^2$ |
| topic | Functional Analysis Complex Variables Operator Algebras 47B20, 47A05, 47B38, 47B33 |
| url | https://arxiv.org/abs/2310.09026 |