A factorization theorem in Banach lattices and its application to Lorentz spaces

Reisner, Sholomo

doi:10.5802/aif.825

Reisner, Sholomo

Annales de l'Institut Fourier, Tome 31 (1981) no. 1, pp. 239-255

Abstract (VO)
Résumé

$p$ -convexity and $q$ -concavity of a Banach lattice $L$ are characterized by factorization of multiplication operators from $L_{q}$ into $L_{p}$ through $L$ . This characterization is applied to calculate the concavity type of Lorentz spaces.

On caractérise la $p$ -convexité et la $q$ -concavité d’un treillis de Banach $L$ à l’aide de la factorisation des opérateurs de multiplication de $L_{q}$ dans $L_{p}$ à travers l’espace $L$ . Cette caractérisation est utilisée pour calculer le type de concavité des espace de Lorentz.

MR Zbl

DOI : 10.5802/aif.825

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     author = {Reisner, Sholomo},
     title = {A factorization theorem in {Banach} lattices and its application to {Lorentz} spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {239--255},
     year = {1981},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {31},
     number = {1},
     doi = {10.5802/aif.825},
     mrnumber = {82g:46066},
     zbl = {0437.46025},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.825/}
}

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Reisner, Sholomo. A factorization theorem in Banach lattices and its application to Lorentz spaces. Annales de l'Institut Fourier, Tome 31 (1981) no. 1, pp. 239-255. doi: 10.5802/aif.825

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