Reflexivity of vector-valued Köthe-Orlicz sequence spaces

Authors : Mohamed Ahmed Ould Sidaty

Pages : 911-923

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Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :Let $E$ be a Banach space, $\lambda$ a perfect sequence space, and $M$ an Orlicz function. Denote by $\lambda \left(E, M\right)_{r}$ the space of all weakly $(M, \lambda)$-summable sequences from $E$ that are the limit of their finite sections. In this paper, we describe the continuous linear functionals on $\lambda \left(E, M\right)_{r}$ in terms of strongly $(N, \lambda^{\ast})$-summable sequences in the dual $E^{*}$ of $E$, and then we give a characterization of the reflexivity of $\lambda \left(E, M\right)$ in terms of that of $\lambda$ and of $E$ and the AK-property.
Keywords : Banach spaces, vector-valued sequence spaces, Orlicz function, duality