| Title:
|
Singlevaluedness of monotone operators on subspaces of GSG spaces (English) |
| Author:
|
Heisler, Martin |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
37 |
| Issue:
|
2 |
| Year:
|
1996 |
| Pages:
|
255-261 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We extend Zajíček's theorem from [Za] about points of singlevaluedness of monotone operators on Asplund spaces. Namely we prove that every monotone operator on a subspace of a Banach space containing densely a continuous image of an Asplund space (these spaces are called GSG spaces) is singlevalued on the whole space except a $\sigma$-cone supported set. (English) |
| Keyword:
|
Asplund spaces |
| Keyword:
|
GSG spaces |
| Keyword:
|
monotone operators |
| Keyword:
|
countable dentability |
| MSC:
|
46B20 |
| MSC:
|
47H04 |
| MSC:
|
47H05 |
| idZBL:
|
Zbl 0849.47025 |
| idMR:
|
MR1399000 |
| . |
| Date available:
|
2009-01-08T18:23:27Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118830 |
| . |
| Reference:
|
Christensen J.P.R., Kenderov P.S.: Dense strong continuity of mappings and the RadonNikodým property.Math. Scand. (1984), 54 70-78. MR 0753064 |
| Reference:
|
Diestel J.: Geometry of Banach Spaces - Selected Topics.Lecture Notes in Mathematics, vol. 485 Springer Verlag (1975). Zbl 0307.46009, MR 0461094 |
| Reference:
|
Fabian M.: Weak Asplund Spaces.Lecture Notes (in preparation) (1995). |
| Reference:
|
Phelps R.R.: Convex Functions, Monotone Operators and Differentiability.Lecture Notes in Math. 1364 Springer Verlag (1989). Zbl 0658.46035, MR 0984602 |
| Reference:
|
Stegall Ch.: The Radon-Nikodým property in conjugate Banach spaces II..Trans. Amer. Math. Soc. (1981), 264 507-519. Zbl 0475.46016, MR 0603779 |
| Reference:
|
Zajíček L.: Smallness of sets of nondifferentiability of convex functions in non-separable Banach spaces.Czech. Math. Journal 41 (116) (1991), 288-296. MR 1105445 |
| . |
