Turkish Journal of Mathematics
DOI
10.3906/mat-1611-113
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
First Page
911
Last Page
923
Recommended Citation
SIDATY, MOHAMED AHMED OULD
(2018)
"Reflexivity of vector-valued Köthe-Orlicz sequence spaces,"
Turkish Journal of Mathematics: Vol. 42:
No.
3, Article 15.
https://doi.org/10.3906/mat-1611-113
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss3/15
