| Title:
|
On maximal monotone operators with relatively compact range (English) |
| Author:
|
Zagrodny, Dariusz |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
105-116 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is shown that every maximal monotone operator on a real Banach space with relatively compact range is of type NI. Moreover, if the space has a separable dual space then every maximally monotone operator $T$ can be approximated by a sequence of maximal monotone operators of type NI, which converge to $T$ in a reasonable sense (in the sense of Kuratowski-Painleve convergence). (English) |
| Keyword:
|
nonlinear operators |
| Keyword:
|
maximal monotone operators |
| Keyword:
|
range of maximal monotone operator |
| Keyword:
|
an approximation method of maximal monotone operators |
| MSC:
|
47H05 |
| idZBL:
|
Zbl 1220.47068 |
| idMR:
|
MR2595075 |
| . |
| Date available:
|
2010-07-20T16:18:55Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140554 |
| . |
| Reference:
|
[1] Debrunner, H., Flor, P.: Ein Erweiterungssatz für monotone Mengen.Arch. Math. 15 (1964), 445-447 German. Zbl 0129.09203, MR 0170189, 10.1007/BF01589229 |
| Reference:
|
[2] Fitzpatrick, S. P., Phelps, R. R.: Bounded approximants to monotone operators on Banach spaces.Ann. Inst. Henri Poincaré 9 (1992), 573-595. Zbl 0818.47052, MR 1191009, 10.1016/S0294-1449(16)30230-X |
| Reference:
|
[3] Holmes, R. B.: Geometric Functional Analysis and its Applications.Springer New York (1975). Zbl 0336.46001, MR 0410335 |
| Reference:
|
[4] Phelps, R. R.: Lecture on maximal monotone operators.Lecture given at Prague/Paseky, Summer school, arXiv:math/9302209v1 [math.FA] (1993). MR 1627478 |
| Reference:
|
[5] Phelps, R. R.: Convex Functions, Monotone Operators and Differentiability. Lecture Notes in Mathematics 1364.Springer Berlin (1989). MR 0984602 |
| Reference:
|
[6] Rockafellar, R. T.: On the virtual convexity of the domain and range of a nonlinear maximal monotone operator.Math. Ann. 185 (1970), 81-90. Zbl 0181.42202, MR 0259697, 10.1007/BF01359698 |
| Reference:
|
[7] Rudin, W.: Functional Analysis (2nd edition).McGraw-Hill New York (1991). MR 1157815 |
| Reference:
|
[8] Simons, S.: From Hahn-Banach to Monotonicity. Lecture Notes in Mathematics 1693 (2nd expanded ed.).Springer Berlin (2008). MR 2386931 |
| Reference:
|
[9] Simons, S.: Minimax and Monotonicity. Lecture Notes in Mathematics 1693.Springer Berlin (1998). MR 1723737 |
| Reference:
|
[10] Zagrodny, D.: The closure of the domain and the range of a maximal monotone multifunction of type NI.Set-Valued Anal. 16 (2008), 759-783. Zbl 1173.47031, MR 2465516, 10.1007/s11228-008-0087-7 |
| Reference:
|
[11] Zeidler, E.: Nonlinear Functional Analysis and its Applications, II/B: Nonlinear Monotone Operators.Springer Berlin (1990). Zbl 0684.47029, MR 1033498 |
| . |
