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Operators and the space of integrable scalar functions with respect to a Fréchet-valued measure

  • Antonio Fernández (a1) and Francisco Naranjo (a1)

Abstract

We consider the space L1 (ν, X) of all real functions that are integrable with respect to a measure v with values in a real Fréchet space X. We study L-weak compactness in this space. We consider the problem of the relationship between the existence of copies of l in the space of all linear continuous operators from a complete DF-space Y to a Fréchet lattice E with the Lebesgue property and the coincidence of this space with some ideal of compact operators. We give sufficient conditions on the measure ν and the space X that imply that L1 (ν, X) has the Dunford-Pettis property. Applications of these results to Fréchet AL-spaces and Köthe sequence spaces are also given.

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References

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Operators and the space of integrable scalar functions with respect to a Fréchet-valued measure

  • Antonio Fernández (a1) and Francisco Naranjo (a1)

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