Operators on analytic function spaces / Opérateurs sur des espaces de fonctions analytiques

Collection Operators on analytic function spaces / Opérateurs sur des espaces de fonctions analytiques

Organizer(s) Fricain, Emmanuel ; Garcia, Stephan Ramon ; Gorkin, Pamela ; Hartmann, Andreas ; Mashreghi, Javad

Date(s) 02/12/2024 - 06/12/2024

linked URL https://conferences.cirm-math.fr/3085.html

00:00:00 / 00:00:00

3 5

Linear isometries on the Fréchet space of holomorphic functions on the open unit disc and the annulus

By Isabelle Chalendar

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.

Information about the video

Date of recording 03/12/2024
Date of publication 13/12/2024
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20273303
Cite this video Chalendar, Isabelle (03/12/2024). 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
URL https://dx.doi.org/10.24350/CIRM.V.20273303

Domain(s)

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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