| Title:
|
A note on weakly Lindelöf determined Banach spaces (English) |
| Author:
|
González, A. |
| Author:
|
Montesinos, V. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
3 |
| Year:
|
2009 |
| Pages:
|
613-621 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that weakly Lindelöf determined Banach spaces are characterized by the existence of a ``full'' projectional generator. Some other results pertaining to this class of Banach spaces are given. (English) |
| Keyword:
|
projectional generator |
| Keyword:
|
projectional resolution of the identity |
| Keyword:
|
weakly Lindelöf determined Banach space |
| Keyword:
|
Markushevich base |
| Keyword:
|
Corson compacta |
| MSC:
|
46B20 |
| MSC:
|
46B26 |
| idZBL:
|
Zbl 1224.46032 |
| idMR:
|
MR2545644 |
| . |
| Date available:
|
2010-07-20T15:29:23Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140504 |
| . |
| Reference:
|
[1] Amir, D., Lindenstrauss, J.: The structure of weakly compact sets in Banach spaces.Ann. of Math. 88 (1968), 35-44. Zbl 0164.14903, MR 0228983, 10.2307/1970554 |
| Reference:
|
[2] Fabian, M.: Gateaux Differentiability of Convex Functions and Topology.Weak Asplund Spaces, John Wiley & Sons, New York (1997). Zbl 0883.46011, MR 1461271 |
| Reference:
|
[3] Fabian, M., Godefroy, G., Montesinos, V., Zizler, V.: Weakly compactly generated spaces and their relatives.J. Math. Anal. and Appl. 297 (2004), 419-455. MR 2088670, 10.1016/j.jmaa.2004.02.015 |
| Reference:
|
[4] Fabian, M., Habala, P., Hájek, P., Pelant, J., Montesinos, V., Zizler, V.: Functional Analysis and Infinite Dimensional Geometry.Canad. Math. Soc. Books in Mathematics, 8, Springer-Verlag, New York (2001). MR 1831176 |
| Reference:
|
[5] Fabian, M., Montesinos, V., Zizler, V.: Weakly compact sets and smooth norms in Banach spaces.Bull. Australian Math. Soc. 65 (2002), 223-230. Zbl 1007.46011, MR 1898536, 10.1017/S0004972700020268 |
| Reference:
|
[6] Fremlin, D. H.: Consequences of Martin's axioms.Cambridge University Press (1984). |
| Reference:
|
[7] Gurarii, V. I., Kadec, M. I.: Minimal systems and quasicomplements in Banach spaces.Soviet Math. Dokl. 3 (1962), 966-968. |
| Reference:
|
[8] Hájek, P., Montesinos, V., Vanderwerff, J., Zizler, V.: Biorthogonal Systems in Banach Spaces.CMS Books in Mathematics, Canadian Mathematical Society, Springer Verlag (2007). MR 2359536 |
| Reference:
|
[9] Rychtář, J.: On biorthogonal systems and Mazur's intersection property.Bull. Austr. Math. Soc. 69 (2004), 107-111. Zbl 1054.46008, MR 2040053, 10.1017/S0004972700034298 |
| Reference:
|
[10] Terenzi, P.: Extension of uniformly minimal M-basic sequences in Banach spaces.J. London Math. Soc. 27 (1983), 500-506. Zbl 0488.46011, MR 0697142, 10.1112/jlms/s2-27.3.500 |
| Reference:
|
[11] Terenzi, P.: On the theory of fundamental bounded biorthogonal systems in Banach spaces.Trans. Amer. Math. Soc. 2 (1987), 497-511. MR 0869217, 10.1090/S0002-9947-1987-0869217-4 |
| Reference:
|
[12] Valdivia, M.: Simultaneous resolutions of the identity operator in normed spaces.Collect. Math. 42 (1991), 265-284. Zbl 0788.47024, MR 1203185 |
| Reference:
|
[13] Valdivia, M.: Biorthogonal systems in certain Banach spaces.Revista Mat. Univ. Complut. Madrid 9 (1996), 191-220. Zbl 0872.46007, MR 1435783 |
| Reference:
|
[14] Vanderwerff, J.: Extensions of Markuševič bases.Math. Z. 219 (1995), 21-30. Zbl 0823.46014, MR 1340846, 10.1007/BF02572347 |
| Reference:
|
[15] Zizler, V.: Nonseparable Banach spaces.Handbook of Banach Spaces, Volume II 1143-1816, Elsevier Sci. B.V. (2003). Zbl 1041.46009, MR 1999608 |
| . |
