Tauberian operators on $L_1(μ)$ spaces

Manuel Gonzalez; Antonio Martínez-Abejón

ArticleOriginal scientific text

Title

Tauberian operators on $L_{1} (μ)$ spaces

Authors ¹, ²

Affiliations

Departamento de Matemáticas, Facultad de Ciencias, Universidad de Cantabria, E-39071 Santander, Spain
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Oviedo, E-33007 Oviedo, Spain

Abstract

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) \frac{*}{L_{1}} (μ) \to Y \frac{*}{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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Title

Tauberian operators on μL1(μ) spaces

Affiliations

Abstract

Bibliography

Tauberian operators on $L_{1} (μ)$ spaces