| Title:
|
A note on the structure of WUR Banach spaces (English) |
| Author:
|
Argyros, S. A. |
| Author:
|
Mercourakis, S. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
399-408 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present an example of a Banach space $E$ admitting an equivalent weakly uniformly rotund norm and such that there is no $\Phi:E\to c_0(\Gamma )$, for any set $\Gamma$, linear, one-to-one and bounded. This answers a problem posed by Fabian, Godefroy, Hájek and Zizler. The space $E$ is actually the dual space $Y^*$ of a space $Y$ which is a subspace of a WCG space. (English) |
| Keyword:
|
WCG Banach space |
| Keyword:
|
weakly uniformly rotund norms |
| Keyword:
|
tree |
| MSC:
|
03E05 |
| MSC:
|
46B20 |
| MSC:
|
46B26 |
| idZBL:
|
Zbl 1123.46011 |
| idMR:
|
MR2174519 |
| . |
| Date available:
|
2009-05-05T16:51:58Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119535 |
| . |
| Reference:
|
[A-M] Argyros S.A., Manoussakis A.: A sequentially unconditional Banach space with few operators.Proc. of LMS, to appear. Zbl 1091.46004 |
| Reference:
|
[A-Me] Argyros S.A., Mercourakis S.: Examples concerning heredity problems of WCG Banach spaces.Proc. Amer. Math. Soc. 133 (2005), 773-785. Zbl 1064.46015, MR 2113927 |
| Reference:
|
[B-R-W] Benyamini Y., Rudin M.E., Wage M.: Continuous images of weakly compact subsets of Banach spaces.Pacific J. Math. 70 (1977), 309-324. Zbl 0374.46011, MR 0625889 |
| Reference:
|
[D-G-Z] Deville R., Godefroy G., Zizler V.: Smoothness and Renormings in Banach Spaces.Pitman Monographs and Surveys in Pure and Applied Math. 64, Longman Scientific & Technical, Harlow, 1993. Zbl 0782.46019, MR 1211634 |
| Reference:
|
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| Reference:
|
[F-H-Z] Fabian M., Hájek P., Zizler V.: On uniform Eberlein compacta and uniformly Gateaux smooth norms.Serdica Math. J. 23 (1997), 351-362. MR 1660997 |
| Reference:
|
[F-Z] Fabian M., Habala P., Hájek P., Montesinos V., Pelant J., Zizler V.: Functional Analysis and Infinite-Dimensional Geometry.CMS Books in Mathematics, Springer, New York, 2001. MR 1831176 |
| Reference:
|
[F-G-H-Z] Fabian M., Godefroy G., Hájek P., Zizler V.: Hilbert generated spaces.J. Funct. Anal. 200 (2003), 301-323. Zbl 1039.46015, MR 1979014 |
| Reference:
|
[F-M-Z] Fabian M., Montesinos V., Zizler V.: Markushevich bases and Eberlein compacts.preprint. |
| Reference:
|
[J] James R.C.: A separable somewhat reflexive Banach space with non-separable dual.Bull. Amer. Math. Soc. 80 (1974), 738-743. MR 0417763 |
| Reference:
|
[J-L] Johnson W.B., Lindenstrauss J.: Some remarks on weakly compactly generated Banach space.Israel J. Math. 17 (1974), 219-230. MR 0417760 |
| Reference:
|
[L-S] Leiderman A.G., Sokolov G.A.: Adequate families of sets and Corson compacts.Comment. Math. Univ. Carolinae 25 (1984), 233-246. Zbl 0586.54022, MR 0768810 |
| Reference:
|
[M] Mercourakis S.: On weakly countably determined Banach spaces.Trans. Amer. Math. Soc. 300 (1987), 307-327. Zbl 0621.46018, MR 0871678 |
| Reference:
|
[Z] Zizler V.: Nonseparable Banach spaces.Handbook of the Geometry of Banach Spaces, Vol. 2, edited by W.B. Johnson and J. Lindenstrauss, North-Holland, Amsterdam, 2003. Zbl 1041.46009, MR 1999613 |
| . |
