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vector-valued sequence space; Köthe dual; GAK-space; Grothendieck space
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.
[1] Leonard I.E.: Banach sequence spaces. J. Math. Anal. Appl. 54 (1976), 245-265. MR 0420216 | Zbl 0343.46010
[2] Wu Congxin, Bu Qingying: 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.
[3] Wu Congxin, Bu Qingying: Banach sequence spaces $\ell _p[X]$ $(1\leq p<\infty)$ and their properties. to appear.
[4] Gupta M., Kamthan P.K., Patterson J.: Duals of generalized sequence spaces. J. Math. Anal. Appl. 82 (1981), 152-168. MR 0626746 | Zbl 0492.46010
[5] Diestel J.: Sequences and Series in Banach Spaces. Graduate Texts in Math. 92, SpringerVerlag, 1984. MR 0737004
[6] Simons S.: Locally reflexivity and $(p,q)$-summing maps. Math. Ann. 198 (1972), 335-344. MR 0326353
[7] Diestel J. Uhl J.J.: Vector Measures. Amer. Math. Soc. Surveys 15, Providence, 1977. MR 0453964
[8] Kamthan P.K., Gupta M.: Sequence Spaces and Series. Lecture Notes 65, Dekker, New York, 1981. MR 0606740 | Zbl 0447.46002
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