Spectrum of weighted composition operators. Part XI. The essential spectra of some weighted composition operators on the disc algebra
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918015500550144 |
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| author | Kitover, Arkady Orhon, Mehmet |
| author_facet | Kitover, Arkady Orhon, Mehmet |
| contents | We obtain a complete description of semi-Fredholm spectra of operators of the form $(Tf)(z) = w(z)f(B(z)$ acting on the disc algebra in the case when $B$ is either elliptic or double parabolic finite Blaschke product of degree $d \geq 2$ and $w$ has no zeros on the unit circle. In the case when $B$ has zeros on the unit circle we provide only some partial results. Our results hint on the possibility of interesting connections between the spectral properties of weighted composition operators and complex dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_17516 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spectrum of weighted composition operators. Part XI. The essential spectra of some weighted composition operators on the disc algebra Kitover, Arkady Orhon, Mehmet Spectral Theory Primary 47B33, Secondary 37F10, 37F15 We obtain a complete description of semi-Fredholm spectra of operators of the form $(Tf)(z) = w(z)f(B(z)$ acting on the disc algebra in the case when $B$ is either elliptic or double parabolic finite Blaschke product of degree $d \geq 2$ and $w$ has no zeros on the unit circle. In the case when $B$ has zeros on the unit circle we provide only some partial results. Our results hint on the possibility of interesting connections between the spectral properties of weighted composition operators and complex dynamics. |
| title | Spectrum of weighted composition operators. Part XI. The essential spectra of some weighted composition operators on the disc algebra |
| topic | Spectral Theory Primary 47B33, Secondary 37F10, 37F15 |
| url | https://arxiv.org/abs/2503.17516 |