Frontiers of Operator Theory / Frontières de la théorie des opérateurs

Collection Frontiers of Operator Theory / Frontières de la théorie des opérateurs

Organizer(s) Badea, Catalin ; Bayart, Frédéric ; Gallardo-Gutiérrez, Eva A. ; Grivaux, Sophie ; Lefèvre, Pascal

Date(s) 29/11/2021 - 03/12/2021

linked URL https://conferences.cirm-math.fr/2388.html

00:00:00 / 00:00:00

4 5

On a duality between Banach spaces and operators

By Mikael de la Salle

Most classical local properties of a Banach spaces (for example type or cotype, UMD), and most of the more recent questions at the intersection with geometric group theory are defined in terms of the boundedness of vector-valued operators between Lp spaces or their subspaces. It was in fact proved by Hernandez in the early 1980s that this is the case of any property that is stable by Lp direct sums and finite representability. His result can be seen as one direction of a bipolar theorem for a non-linear duality between Banach spaces and operators. I will present the other direction and describe the bipolar of any class of operators for this duality. The talk will be based on my preprint arxiv:2101.07666.

Information about the video

Date of recording 30/11/2021
Date of publication 03/01/2022
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19855603
Cite this video de la Salle, Mikael (30/11/2021). On a duality between Banach spaces and operators. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19855603
URL https://dx.doi.org/10.24350/CIRM.V.19855603

Domain(s)

Functional Analysis

Bibliography

DE LA SALLE, Mikael. A duality operators/Banach spaces. arXiv preprint arXiv:2101.07666, 2021. - https://arxiv.org/abs/2101.07666

MSC codes

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