Sur quelques extensions au cadre Banachique de la notion d'opérateur de Hilbert-Schmidt
| hal.structure.identifier | Université des Comores | |
| dc.contributor.author | ABDILLAH, Said Amana | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ESTERLE, Jean | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | HAAK, Bernhard Hermann | |
| dc.date.accessioned | 2024-04-04T03:22:17Z | |
| dc.date.available | 2024-04-04T03:22:17Z | |
| dc.date.created | 2014 | |
| dc.date.issued | 2015 | |
| dc.identifier.issn | 0039-3223 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194741 | |
| dc.description.abstractEn | In this work we discuss several ways to extend to the context of Banach spaces the notion of Hilbert-Schmidt operators: $p$-summing operators, $\gamma$-summing or $\gamma$-radonifying operators, weakly $*1$-nuclear operators and classes of operators defined via factorization properties. We introduce the class $PS_2(E; F)$ of pre-Hilbert-Schmidt operators as the class of all operators $u:E\to F$ such that $w\circ u \circ v$ is Hilbert-Schmidt for every bounded operator $v: H_1\to E$ and every bounded operator $w:F\to H_2$, where $H_1$ et $H_2$ are Hilbert spaces. Besides the trivial case where one of the spaces $E$ or $F$ is a "Hilbert-Schmidt space", this space seems to have been described only in the easy situation where one of the spaces $E$ or $F$ is a Hilbert space. | |
| dc.description.sponsorship | Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013 | |
| dc.language.iso | fr | |
| dc.publisher | Instytut Matematyczny - Polska Akademii Nauk | |
| dc.rights.uri | http://hal.archives-ouvertes.fr/licences/copyright/ | |
| dc.subject.en | Grothendieck's inequality | |
| dc.subject.en | Banach spaces | |
| dc.subject.en | Hilbert-Schmidt operators | |
| dc.subject.en | $p$-summing operators | |
| dc.subject.en | almost summing operators | |
| dc.subject.en | $\gamma$-summing operators | |
| dc.subject.en | $\gamma$-radonifying operators | |
| dc.title | Sur quelques extensions au cadre Banachique de la notion d'opérateur de Hilbert-Schmidt | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| dc.identifier.arxiv | 1406.7546 | |
| bordeaux.journal | Studia Mathematica | |
| bordeaux.page | 192-218 | |
| bordeaux.volume | 3 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 227 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01015841 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01015841v1 | |
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