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Linear isometries on the Fréchet space of holomorphic functions on the open unit disc and the annulus
Multi angle
Authors : Chalendar, Isabelle (Author of the conference)
CIRM (Publisher )
30H05 - Spaces and algebras of analytic functions, See also {32E25, 46Exx, 46J15}
47A10 - Spectrum and resolvent of linear operators
47B33 - Composition operators
CIRM (Publisher )
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Abstract :
Let $\mathrm{X}$ be a topological space of holomorphic functions on the open unit disc $D$. The study of the geometry of a space $X$ is centered on the identification of the linear isometries on $\mathrm{X}$, and there is an obvious connection between weighted composition operators and isometries. This connection can be traced back to Banach himself and emphasized by Forelli, El-Gebeily, Wolfe, Kolaski, Cima, Wogen, Colonna and many others. A characterisation is given of all the linear isometries of Hol($\Omega$), the Fr´ echet space of all holomorphic functions on $\Omega$ when $\Omega$ is the unit disc or an annulus, endowed with one of the standard metrics. Further, the larger class of operators isometric when restricted to one of the defining seminorms is identified. This is a joint work with Lucas Oger and Jonathan Partington.
Keywords : Fréchet space; holomorphic functions; isometry; annulus; weighted composition operator; spectrum
MSC Codes : Keywords : Fréchet space; holomorphic functions; isometry; annulus; weighted composition operator; spectrum
30H05 - Spaces and algebras of analytic functions, See also {32E25, 46Exx, 46J15}
47A10 - Spectrum and resolvent of linear operators
47B33 - Composition operators
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Information on the Video
Film maker : Récanzone, LucaLanguage : English Available date : 14/12/2024 Conference Date : 03/12/2024 Subseries : Research talks arXiv category : Functional Analysis ; Complex Variables Mathematical Area(s) : Analysis and its Applications Format : MP4 (.mp4) - HD Video Time : 00:37:43 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-12-03_Chalendar.mp4 
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Information on the Event
Event Title : Operators on analytic function spaces / Opérateurs sur des espaces de fonctions analytiquesEvent Organizers : Fricain, Emmanuel ; Garcia, Stephan Ramon ; Gorkin, Pamela ; Hartmann, Andreas ; Mashreghi, Javad Dates : 02/12/2024 - 06/12/2024 Event Year : 2024 Event URL : https://conferences.cirm-math.fr/3085.html
Citation Data
DOI : 10.24350/CIRM.V.20273303Cite this video as: Chalendar, Isabelle (2024). Linear isometries on the Fréchet space of holomorphic functions on the open unit disc and the annulus. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20273303 URI : http://dx.doi.org/10.24350/CIRM.V.20273303 |
See Also
- [Multi angle] Point evaluation in Paley–Wiener spaces / Author of the conference Seip, Kristian.
- [Multi angle] Some recent results on generic properties of contractions on Banach spaces / Author of the conference Grivaux, Sophie.
- [Multi angle] Common range of co-analytic Toeplitz operators on the Drury-Arveson space / Author of the conference McCarthy, John.
- [Multi angle] von Neumann's inequality on the polydisc / Author of the conference Hartz, Michael.
Bibliography
- CHALENDAR, Isabelle, OGER, Lucas, et PARTINGTON, Jonathan R. Linear isometries on the annulus: description and spectral properties. arXiv preprint arXiv:2409.16105, 2024. - https://doi.org/10.48550/arXiv.2409.16105
- ARENDT, Wolfgang, BERNARD, Eddy, CELARIES, Benjamin, et al. Spectral properties of weighted composition operators on Hol(\mathbb{D}) induced by rotations, Indiana Univ. Math. J. 72 (2023), 1789-1820 - https://doi.org/10.1512/iumj.2023.72.9511
- CHALENDAR, Isabelle, OGER, Lucas, et PARTINGTON, Jonathan R. Linear isometries of Hol (D). Journal of Mathematical Analysis and Applications, 2024, p. 128619. - https://doi.org/10.1016/j.jmaa.2024.128619
- CHALENDAR, Isabelle, OGER, Lucas, et PARTINGTON, Jonathan R., Linear and isometries on the annulus: description and spectral properties, submitted -
- EL-GEBEILY, Mohamad et WOLFE, John. Isometries of the disc algebra. Proceedings of the American Mathematical Society, 1985, vol. 93, no 4, p. 697-702. - https://doi.org/10.1090/S0002-9939-1985-0776205-9
- FORELLI, Frank. The isometries of Hp. Canadian Journal of Mathematics, 1964, vol. 16, p. 721-728. - https://doi.org/10.4153/CJM-1964-068-3
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