| Title:
|
Antiproximinal sets in the Banach space $c(X)$ (English) |
| Author:
|
Cobzaş, S. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
2 |
| Year:
|
1997 |
| Pages:
|
247-253 |
| . |
| Category:
|
math |
| . |
| Summary:
|
If $X$ is a Banach space then the Banach space $c(X)$ of all $X$-valued convergent sequences contains a nonvoid bounded closed convex body $V$ such that no point in $C(X)\setminus V$ has a nearest point in $V$. (English) |
| Keyword:
|
antiproximinal sets |
| Keyword:
|
best approximation |
| MSC:
|
41A50 |
| MSC:
|
41A65 |
| MSC:
|
46B20 |
| MSC:
|
46B99 |
| idZBL:
|
Zbl 0887.41029 |
| idMR:
|
MR1455491 |
| . |
| Date available:
|
2009-01-08T18:30:33Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118922 |
| . |
| Reference:
|
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| Reference:
|
[2] Cobzaş S.: Very non-proximinal sets in $c_0$ (in Romanian).Rev. Anal. Numer. Teoria Approx. 2 (1973), 137-141. MR 0393980 |
| Reference:
|
[3] Cobzaş S.: Antiproximinal sets in some Banach spaces.Math. Balkanica 4 (1974), 79-82. MR 0377381 |
| Reference:
|
[4] Cobzaş S.: Convex antiproximinal sets in the spaces $c_0$ and $c$ (in Russian).Matem. Zametki 17 (1975), 449-457. MR 0407567 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Dunford N., Schwartz J.T.: Linear Operators I. General Theory.Interscience, New York, 1958. Zbl 0084.10402, MR 0117523 |
| Reference:
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[9] Edelstein M., Thompson A.C.: Some results on nearest points and support properties of convex sets in $c_0$.Pacific J. Math. 40 (1972), 553-560. MR 0308741 |
| Reference:
|
[10] Fonf V.P.: On antiproximinal sets in spaces of continuous functions on compacta (in Russian).Matem. Zametki 33 (1983), 549-558. MR 0704442 |
| Reference:
|
[11] Fonf V.P.: On strongly antiproximinal sets in Banach spaces (in Russian).Matem. Zametki 47 (1990), 130-136. MR 1048552 |
| Reference:
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[12] Holmes R.B.: Geometric Functional Analysis and its Applications.Springer Verlag, BerlinHeidelberg-New York, 1975. Zbl 0336.46001, MR 0410335 |
| Reference:
|
[13] Klee V.: Remarks on nearest points in normed linear spaces.Proc. Colloq. Convexity, Copenhagen 1965, pp.161-176, Copenhagen, 1967. Zbl 0156.36303, MR 0223859 |
| Reference:
|
[14] Phelps R.R.: Subreflexive normed linear spaces.Archiv der Math. 8 (1957), 444-450. MR 0099588 |
| Reference:
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| Reference:
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[16] Sierpinski W.: Cardinal and Ordinal Numbers.Warszawa, 1965. Zbl 0131.24801, MR 0194339 |
| Reference:
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| Reference:
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[18] Stečkin S.B.: On the approximation properties of sets in normed linear spaces (in Russian).Rev. Math. Pures et Appl. 8 (1963), 5-18. MR 0155168 |
| Reference:
|
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| Reference:
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[20] Werner D.: Funktionalanalysis.Springer Verlag, Berlin-Heidelberg-New York, 1995. Zbl 1161.46001, MR 1787146 |
| . |
