English
Linear isometries on the Fréchet space of holomorphic functions on the open unit disc and the annulus
Multi angle
Auteurs : Chalendar, Isabelle (Auteur de la Conférence)
CIRM (Editeur )
30H05 - Spaces and algebras of analytic functions, See also {32E25, 46Exx, 46J15}
47A10 - Spectrum and resolvent of linear operators
47B33 - Composition operators
CIRM (Editeur )
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Résumé :
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
Codes MSC : 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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Informations sur la Vidéo
Réalisateur : Récanzone, LucaLangue : Anglais Date de publication : 14/12/2024 Date de captation : 03/12/2024 Sous collection : Research talks arXiv category : Functional Analysis ; Complex Variables Domaine : Analysis and its Applications Format : MP4 (.mp4) - HD Durée : 00:37:43 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2024-12-03_Chalendar.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Operators on analytic function spaces / Opérateurs sur des espaces de fonctions analytiquesOrganisateurs de la rencontre : Fricain, Emmanuel ; Garcia, Stephan Ramon ; Gorkin, Pamela ; Hartmann, Andreas ; Mashreghi, Javad Dates : 02/12/2024 - 06/12/2024 Année de la rencontre : 2024 URL Congrès : https://conferences.cirm-math.fr/3085.html
Données de citation
DOI : 10.24350/CIRM.V.20273303Citer cette vidéo: 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 |
Voir aussi
- [Multi angle] Point evaluation in Paley–Wiener spaces / Auteur de la Conférence Seip, Kristian.
- [Multi angle] Some recent results on generic properties of contractions on Banach spaces / Auteur de la Conférence Grivaux, Sophie.
- [Multi angle] Common range of co-analytic Toeplitz operators on the Drury-Arveson space / Auteur de la Conférence McCarthy, John.
- [Multi angle] von Neumann's inequality on the polydisc / Auteur de la Conférence Hartz, Michael.
Bibliographie
- 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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