Tauberian operators on $L_1(μ)$ spaces

González, Manuel; Martínez-Abejón, Antonio

Tauberian operators on

L_{1} (μ)

spaces

González, Manuel ; Martínez-Abejón, Antonio

Studia Mathematica, Tome 122 (1997), p. 289-303 / Harvested from The Polish Digital Mathematics Library

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Résumé

We characterize tauberian operators $T : L_{1} (μ) \to Y$ in terms of the images of disjoint sequences and in terms of the image of the dyadic tree in $L_{1} [0, 1]$ . As applications, we show that the class of tauberian operators is stable under small norm perturbations and that its perturbation class coincides with the class of all weakly precompact operators. Moreover, we prove that the second conjugate of a tauberian operator $T : L_{1} (μ) \to Y$ is also tauberian, and the induced operator $T ̃ : L_{1} (μ) * * / L_{1} (μ) \to Y * * / Y$ is an isomorphism into. Also, we show that $L_{1} (μ)$ embeds isomorphically into the quotient of $L_{1} (μ)$ by any of its reflexive subspaces.

Publié le : 1997-01-01

Zbl 0907.47026

EUDML-ID : urn:eudml:doc:216439

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     author = {Manuel Gonz\'alez and Antonio Mart\'\i nez-Abej\'on},
     title = {Tauberian operators on $L\_1($\mu$)$ spaces},
     journal = {Studia Mathematica},
     volume = {122},
     year = {1997},
     pages = {289-303},
     zbl = {0907.47026},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv125i3p289bwm}
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González, Manuel; Martínez-Abejón, Antonio. Tauberian operators on $L_1(μ)$ spaces. Studia Mathematica, Tome 122 (1997) pp. 289-303. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv125i3p289bwm/

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