| Title:
|
Köthe dual of Banach sequence spaces $\ell_p[X]$ $(1\le p<\infty)$ and Grothendieck space (English) |
| Author:
|
Wu, Congxin |
| Author:
|
Bu, Qingying |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
34 |
| Issue:
|
2 |
| Year:
|
1993 |
| Pages:
|
265-273 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
vector-valued sequence space |
| Keyword:
|
Köthe dual |
| Keyword:
|
GAK-space |
| Keyword:
|
Grothendieck space |
| MSC:
|
46A45 |
| MSC:
|
46B16 |
| MSC:
|
46B20 |
| MSC:
|
46B28 |
| MSC:
|
46B45 |
| idZBL:
|
Zbl 0785.46009 |
| idMR:
|
MR1241736 |
| . |
| Date available:
|
2009-01-08T18:03:19Z |
| Last updated:
|
2023-07-17 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118580 |
| . |
| Reference:
|
[1] Leonard I.E.: Banach sequence spaces.J. Math. Anal. Appl. 54 (1976), 245-265. Zbl 0343.46010, MR 0420216, 10.1016/0022-247X(76)90248-1 |
| Reference:
|
[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. |
| Reference:
|
[3] Wu Congxin, Bu Qingying: Banach sequence spaces $\ell _p[X]$ $(1\leq p<\infty)$ and their properties.to appear. |
| Reference:
|
[4] Gupta M., Kamthan P.K., Patterson J.: Duals of generalized sequence spaces.J. Math. Anal. Appl. 82 (1981), 152-168. Zbl 0492.46010, MR 0626746, 10.1016/0022-247X(81)90230-4 |
| Reference:
|
[5] Diestel J.: Sequences and Series in Banach Spaces.Graduate Texts in Math. 92, SpringerVerlag, 1984. MR 0737004 |
| Reference:
|
[6] Simons S.: Locally reflexivity and $(p,q)$-summing maps.Math. Ann. 198 (1972), 335-344. MR 0326353, 10.1007/BF01419563 |
| Reference:
|
[7] Diestel J. Uhl J.J.: Vector Measures.Amer. Math. Soc. Surveys 15, Providence, 1977. MR 0453964 |
| Reference:
|
[8] Kamthan P.K., Gupta M.: Sequence Spaces and Series.Lecture Notes 65, Dekker, New York, 1981. Zbl 0447.46002, MR 0606740 |
| . |
