Tauberian operators on $L_1(μ)$ spaces

• Autorzy: Manuel González , Antonio Martínez-Abejón
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47B38: Operators on function spaces (general)
• 47A35: Ergodic theory
• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 125
• Numer: 3
• Strony: 289-303

Daty

wydano

1997

otrzymano

1996-12-02

poprawiono

1997-05-12

Twórcy

autor

Manuel González

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

autor

Antonio Martínez-Abejón

• Departamento de Matemáticas, Facultad de Ciencias, Universidad de Oviedo, E-33007 Oviedo, Spain

Bibliografia

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