In this paper, we show the representation of Köthe dual of Banach sequence spaces $\ell _p[X]$ $(1\leq p< \infty )$ and give a characterization of that the spaces $\ell _p[X]$ $(1< p< \infty )$ are Grothendieck spaces.
@article{118580, author = {Cong Xin Wu and Qing Ying Bu}, title = {K\"othe dual of Banach sequence spaces $\ell\_p[X]$ $(1\le p<\infty)$ and Grothendieck space}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {34}, year = {1993}, pages = {265-273}, zbl = {0785.46009}, mrnumber = {1241736}, language = {en}, url = {http://dml.mathdoc.fr/item/118580} }
Wu, Cong Xin; Bu, Qing Ying. Köthe dual of Banach sequence spaces $\ell_p[X]$ $(1\le p<\infty)$ and Grothendieck space. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 265-273. http://gdmltest.u-ga.fr/item/118580/
Banach sequence spaces, J. Math. Anal. Appl. 54 (1976), 245-265. (1976) | MR 0420216 | Zbl 0343.46010
The vector-valued sequence spaces $\ell _p(X)$ $(1\leq p<\infty)$ and Banach spaces not containing a copy of $c_0$, A Friendly Collection of Mathematical Papers I, Jilin Univ. Press, Changchun, China, 1990, 9-16.
Banach sequence spaces $\ell _p[X]$ $(1\leq p<\infty)$ and their properties, to appear.
Duals of generalized sequence spaces, J. Math. Anal. Appl. 82 (1981), 152-168. (1981) | MR 0626746 | Zbl 0492.46010
Sequences and Series in Banach Spaces, Graduate Texts in Math. 92, SpringerVerlag, 1984. | MR 0737004
Locally reflexivity and $(p,q)$-summing maps, Math. Ann. 198 (1972), 335-344. (1972) | MR 0326353
Vector Measures, Amer. Math. Soc. Surveys 15, Providence, 1977. | MR 0453964
Sequence Spaces and Series, Lecture Notes 65, Dekker, New York, 1981. | MR 0606740 | Zbl 0447.46002