Reflexivity and AK-property of certain vector sequence spaces

Ould  Sidaty, M. A.

Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, p. 579-583 / Harvested from Project Euclid

Résumé

Let $E$ be a Banach space and $\Lambda$ a Banach perfect sequence space. Denote by $\Lambda (E)$ the space of all $\Lambda$-summable sequences from $E$. In this note it is proved that $\Lambda (E)$ is reflexive if and only if $\Lambda$ and $E$ are reflexive and each member of $\Lambda (E)$ is the limit of its finite sections.

Publié le : 2003-09-14
Classification: sequence spaces, normed spaces, reflexivity, compact operators, AK-spaces, 46A17, 46B35

@article{1070645803,
     author = {Ould  Sidaty, M. A.},
     title = {Reflexivity and AK-property of certain vector sequence spaces},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {10},
     number = {1},
     year = {2003},
     pages = { 579-583},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1070645803}
}

Ould  Sidaty, M. A. Reflexivity and AK-property of certain vector sequence spaces. Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, pp.  579-583. http://gdmltest.u-ga.fr/item/1070645803/