A duality operators/Banach spaces
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| Název: | A duality operators/Banach spaces |
|---|---|
| Autoři: | de La Salle, Mikael |
| Přispěvatelé: | de la Salle, Mikael, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure de Lyon (ENS de Lyon), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Équations aux dérivées partielles, analyse (EDPA), Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), ANR-16-CE40-0022,AGIRA,Actions de Groupes, Isométries, Rigidité et Aléa(2016), ANR-19-CE40-0002,ANCG,Analyse non commutative sur les groupes et les groupes quantiques(2019), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010) |
| Zdroj: | Annales de l'Institut Fourier. :1-43 |
| Publication Status: | Preprint |
| Informace o vydavateli: | Cellule MathDoc/Centre Mersenne, 2025. |
| Rok vydání: | 2025 |
| Témata: | Mathematics - Functional Analysis, [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA], [MATH.MATH-FA] Mathematics [math]/Functional Analysis [math.FA], FOS: Mathematics, 0101 mathematics, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], [MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA], 01 natural sciences, [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR], [MATH.MATH-GR] Mathematics [math]/Group Theory [math.GR], Functional Analysis (math.FA) |
| Popis: | To a pair (T,X) of an operator T between subspaces of L p spaces and a Banach space X we can associate a finite or infinite number, the norm ∥T X ∥ of T between the subspaces of the X-valued L p spaces. Given such an operator T, we characterize all the operators S for which the implication ∥T X ∥<∞⇒∥S X ∥<∞ holds.This is a form of the bipolar theorem for a duality between the class of Banach spaces and the class of operators between subspaces of L p spaces, essentially introduced by Pisier. The methods we introduce allow us to recover also the other direction – characterizing the bipolar of a set of Banach spaces –, which had been obtained by Hernandez in 1983. |
| Druh dokumentu: | Article |
| Jazyk: | English |
| ISSN: | 1777-5310 |
| DOI: | 10.5802/aif.3730 |
| DOI: | 10.48550/arxiv.2101.07666 |
| Přístupová URL adresa: | http://arxiv.org/abs/2101.07666 https://hal.science/hal-03264856v1 |
| Rights: | CC BY SA |
| Přístupové číslo: | edsair.doi.dedup.....ed9caebc4d00aa9e5cff0f040e76d692 |
| Databáze: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | To a pair (T,X) of an operator T between subspaces of L p spaces and a Banach space X we can associate a finite or infinite number, the norm ∥T X ∥ of T between the subspaces of the X-valued L p spaces. Given such an operator T, we characterize all the operators S for which the implication ∥T X ∥<∞⇒∥S X ∥<∞ holds.This is a form of the bipolar theorem for a duality between the class of Banach spaces and the class of operators between subspaces of L p spaces, essentially introduced by Pisier. The methods we introduce allow us to recover also the other direction – characterizing the bipolar of a set of Banach spaces –, which had been obtained by Hernandez in 1983. |
|---|---|
| ISSN: | 17775310 |
| DOI: | 10.5802/aif.3730 |