# Tauberian operators on ${L}_{1}\left(\mu \right)$ spaces

Manuel González; Antonio Martínez-Abejón

Studia Mathematica (1997)

- Volume: 125, Issue: 3, page 289-303
- ISSN: 0039-3223

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topGonzález, Manuel, and Martínez-Abejón, Antonio. "Tauberian operators on $L_1(μ)$ spaces." Studia Mathematica 125.3 (1997): 289-303. <http://eudml.org/doc/216439>.

@article{González1997,

abstract = {We characterize tauberian operators $T:L_1(μ) → Y$ 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 $T:L_1(μ) → Y$ is also tauberian, and the induced operator $T̃: L_1(μ)**/L_1(μ) → Y**/Y$ 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.},

author = {González, Manuel, Martínez-Abejón, Antonio},

journal = {Studia Mathematica},

keywords = {Tauberian operators; images of disjoint sequences; image of the dyadic tree; weakly precompact operators; reflexive subspaces},

language = {eng},

number = {3},

pages = {289-303},

title = {Tauberian operators on $L_1(μ)$ spaces},

url = {http://eudml.org/doc/216439},

volume = {125},

year = {1997},

}

TY - JOUR

AU - González, Manuel

AU - Martínez-Abejón, Antonio

TI - Tauberian operators on $L_1(μ)$ spaces

JO - Studia Mathematica

PY - 1997

VL - 125

IS - 3

SP - 289

EP - 303

AB - We characterize tauberian operators $T:L_1(μ) → Y$ 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 $T:L_1(μ) → Y$ is also tauberian, and the induced operator $T̃: L_1(μ)**/L_1(μ) → Y**/Y$ 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.

LA - eng

KW - Tauberian operators; images of disjoint sequences; image of the dyadic tree; weakly precompact operators; reflexive subspaces

UR - http://eudml.org/doc/216439

ER -

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