| Title:
|
Remarks on continuous images of Radon-Nikodým compacta (English) |
| Author:
|
Fabian, M. |
| Author:
|
Heisler, M. |
| Author:
|
Matoušková, E. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
39 |
| Issue:
|
1 |
| Year:
|
1998 |
| Pages:
|
59-69 |
| . |
| Category:
|
math |
| . |
| Summary:
|
A family of compact spaces containing continuous images of Radon-Nikod'ym compacta is introduced and studied. A family of Banach spaces containing subspaces of Asplund generated (i.e., GSG) spaces is introduced and studied. Further, for a continuous image of a Radon-Nikod'ym compact $K$ we prove: If $K$ is totally disconnected, then it is Radon-Nikod'ym compact. If $K$ is adequate, then it is even Eberlein compact. (English) |
| Keyword:
|
Asplund generated space |
| Keyword:
|
continuous image of Radon-Nikodym compact |
| Keyword:
|
totally disconnected compact |
| Keyword:
|
adequate compact |
| Keyword:
|
Eberlein compact |
| MSC:
|
46B22 |
| idZBL:
|
Zbl 0937.46015 |
| idMR:
|
MR1622332 |
| . |
| Date available:
|
2009-01-08T18:39:02Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118985 |
| . |
| Reference:
|
[A1] Argyros S.: Weakly Lindelöf determined Banach spaces not containing $\ell_1$.preprint. |
| Reference:
|
[A2] Argyros S.: Private communication.. |
| Reference:
|
[BRW] 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:
|
[DS] Dunford N., Schwartz J.T.: Linear Operators, Part I.Interscience Publ., New York, 1958. Zbl 0635.47001 |
| Reference:
|
[F] Fabian M.: Gâteaux Differentiability of Convex Functions and Topology - Weak Asplund Spaces.John Wiley & Sons, Interscience, New York, 1997. Zbl 0883.46011, MR 1461271 |
| Reference:
|
[Gr] Grothendieck A.: Produits tensoriels et espaces nucleaires.Memoirs Amer. Math. Soc., No. 16, 1955. MR 0075539 |
| Reference:
|
[H1] Heisler M.: Singlevaluedness of monotone operators on subspaces of GSG spaces.Comment. Math. Univ. Carolinae 37 (1996), 255-261. Zbl 0849.47025, MR 1399000 |
| Reference:
|
[H2] Heisler M.: Some aspects of differentiability and geometry on Banach spaces.PhD. Thesis, Prague, 1996. |
| Reference:
|
[N1] Namioka I.: Eberlein and Radon-Nikodým compact spaces.Lecture Notes at University College, London, 1985. MR 0963600 |
| Reference:
|
[N2] Namioka I.: Radon-Nikodým compact spaces and fragmentability.Mathematika 34 (1987), 258-281. Zbl 0654.46017, MR 0933504 |
| Reference:
|
[NP] Namioka I., Phelps R.R.: Banach spaces which are Asplund spaces.Duke Math. J. 42 (1975), 735-750. Zbl 0332.46013, MR 0390721 |
| Reference:
|
[OSV] Orihuela J., Schachermayer W., Valdivia M.: Every Radon-Nikodým Corson compact is Eberlein compact.Studia Math. 98 (1991), 157-174. MR 1100920 |
| Reference:
|
[Ph] Phelps R.R.: Convex functions, monotone operators and differentiability.Lect. Notes Math., No. 1364, 2nd Edition, Springer Verlag, Berlin, 1993. Zbl 0921.46039, MR 1238715 |
| Reference:
|
[Ro] Rosenthal H.: The heredity problem for weakly compactly generated Banach spaces.Comp. Math. 28 (1974), 83-111. Zbl 0298.46013, MR 0417762 |
| Reference:
|
[St1] Stegall Ch.: The Radon-Nikodým property in conjugate Banach spaces II.Trans. Amer. Math. Soc. 264 (1981), 507-519. Zbl 0475.46016, MR 0603779 |
| Reference:
|
[St2] Stegall Ch.: More facts about conjugate Banach spaces with the Radon-Nikodým property II.Acta Univ. Carolinae - Math. et Phys. 32 (1991), 47-54. Zbl 0773.46008, MR 1146766 |
| Reference:
|
[T] Talagrand M.: Espaces de Banach faiblement $K$-analytiques.Annals of Math. 110 (1978), 407-438. MR 0554378 |
| . |
