Tauberian operators on L 1 ( μ ) spaces

Manuel González; Antonio Martínez-Abejón

Studia Mathematica (1997)

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

Abstract

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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 T ̃ : 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.

How to cite

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González, 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 -

References

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