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) 11/29/21 - 12/3/21
linked URL https://conferences.cirm-math.fr/2388.html
00:00:00 / 00:00:00
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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.

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Citation data

  • DOI 10.24350/CIRM.V.19855603
  • Cite this video de la Salle Mikael (11/30/21). 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

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