| Title:
|
Generalized first class selectors for upper semi-continuous set-valued maps in Banach spaces (English) |
| Author:
|
Hansell, R. W. |
| Author:
|
Oncina, L. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
145-155 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we deal with weakly upper semi-continuous set-valued maps, taking arbitrary non-empty values, from a non-metric domain to a Banach space. We obtain selectors having the point of continuity property relative to the norm topology for a large class of compact spaces as a domain. Exact conditions under which the selector is of the first Borel class are also investigated. (English) |
| Keyword:
|
measurable selectors |
| Keyword:
|
upper semi-continuous maps |
| Keyword:
|
point of continuity property |
| MSC:
|
46B22 |
| MSC:
|
46B99 |
| MSC:
|
47H04 |
| idZBL:
|
Zbl 1081.46016 |
| idMR:
|
MR2121662 |
| . |
| Date available:
|
2009-09-24T11:21:38Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127965 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] W. R. Hansell: First class selectors for upper semi-continuous multifunctions.J. Funct. Anal. 75 (1987), 382–395. Zbl 0644.54014, MR 0916758, 10.1016/0022-1236(87)90102-9 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[7] R. W. Hansell, J. E. Jayne, and M. Talagrand: First class selector for weakly upper semi-continuous multivalued maps in Banach spaces.J. Reine Angew. Math. 361 (1985), 201–220. MR 0807260 |
| Reference:
|
[8] J. E. Jayne, J. Orihuela, A. J. Pallarés, and G. Vera: $\sigma $-fragmentability of multivalued maps and selection theorems.J. Funct. Anal. 117 (1993), 243–273. MR 1244937, 10.1006/jfan.1993.1127 |
| Reference:
|
[9] J. E. Jayne, C. A. Rogers: Borel selectors for upper semi-continuous set-valued maps.Acta. Math. 155 (1985), 41–79. MR 0793237, 10.1007/BF02392537 |
| Reference:
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[10] I. Namioka: Radon-Nikodým compact spaces and fragmentability.Mathematika 34 (1989), 258–281. MR 0933504 |
| Reference:
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[11] L. Oncina: Descriptive Banach spaces and Eberlein compacta.Doctoral Thesis, Universidad de Murcia, 1999. |
| Reference:
|
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| Reference:
|
[13] V. V. Srivatsa: Baire class 1 selectors for upper-semicontinuous set-valued maps.Trans. Amer. Math. Soc. 337 (1993), 609–624. Zbl 0822.54017, MR 1140919 |
| Reference:
|
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| . |
