Geodesic
Tauberian operators on $L_1(μ)$ spaces
Studia Mathematica, Tome 125 (1997) no. 3, pp. 289-303
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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 $T̃: L_1(μ)**/L_1(μ) → Y**/Y$ 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. 
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Manuel Gonzalez;  . Tauberian operators on $L_1(μ)$ spaces. Studia Mathematica, Tome 125 (1997) no. 3, pp. 289-303. doi: 10.4064/sm-125-3-289-303

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