Antiproximinal sets in the Banach space $c(X)$
Cobzaş, S.
Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997), p. 247-253 / Harvested from Czech Digital Mathematics Library
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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 $V$.

Publié le : 1997-01-01
Classification:  41A50,  41A65,  46B20,  46B99 
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     author = {S. Cobza\c s},
     title = {Antiproximinal sets in the Banach space $c(X)$},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {38},
     year = {1997},
     pages = {247-253},
     zbl = {0887.41029},
     mrnumber = {1455491},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118922}
}

Cobzaş, S. Antiproximinal sets in the Banach space $c(X)$. Commentationes Mathematicae Universitatis Carolinae, Tome 38 (1997) pp. 247-253. http://gdmltest.u-ga.fr/item/118922/

Chakalov V.L. Extremal elements in some normed spaces, Comptes Rendus Acad. Bulgare des Sciences 36 (1983), 173-176. (1983) | MR 0709005

Cobzaş S. Very non-proximinal sets in $c_0$ (in Romanian), Rev. Anal. Numer. Teoria Approx. 2 (1973), 137-141. (1973) | MR 0393980

Cobzaş S. Antiproximinal sets in some Banach spaces, Math. Balkanica 4 (1974), 79-82. (1974) | MR 0377381

Cobzaş S. Convex antiproximinal sets in the spaces $c_0$ and $c$ (in Russian), Matem. Zametki 17 (1975), 449-457. (1975) | MR 0407567

Cobzaş S. Antiproximinal sets in Banach spaces of continuous functions, Anal. Numér. Théorie Approx. 5 (1976), 127-143. (1976) | MR 0477577

Cobzaş S. Antiproximinal sets in Banach spaces of $c_0$-type, Rev. Anal. Numér. Théorie Approx. 7 (1978), 141-145. (1978) | MR 0530744

Cobzaş S. Support functionals of the unit ball in Banach spaces of bounded functions, Seminar on Mathematical Analysis, Babeş-Bolyai University Research Seminaries, Preprint nr. 4, pp.85-90, Cluj-Napoca, 1986.

Dunford N.; Schwartz J.T. Linear Operators I. General Theory, Interscience, New York, 1958. | MR 0117523 | Zbl 0084.10402

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. (1972) | MR 0308741

Fonf V.P. On antiproximinal sets in spaces of continuous functions on compacta (in Russian), Matem. Zametki 33 (1983), 549-558. (1983) | MR 0704442

Fonf V.P. On strongly antiproximinal sets in Banach spaces (in Russian), Matem. Zametki 47 (1990), 130-136. (1990) | MR 1048552

Holmes R.B. Geometric Functional Analysis and its Applications, Springer Verlag, BerlinHeidelberg-New York, 1975. | MR 0410335 | Zbl 0336.46001

Klee V. Remarks on nearest points in normed linear spaces, Proc. Colloq. Convexity, Copenhagen 1965, pp.161-176, Copenhagen, 1967. | MR 0223859 | Zbl 0156.36303

Phelps R.R. Subreflexive normed linear spaces, Archiv der Math. 8 (1957), 444-450. (1957) | MR 0099588

Phelps R.R. Some subreflexive Banach spaces, Archiv der Math. 10 (1959), 162-169. (1959) | MR 0107162 | Zbl 0087.10704

Sierpinski W. Cardinal and Ordinal Numbers, Warszawa, 1965. | MR 0194339 | Zbl 0131.24801

Singer I. Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces, Editura Academiei and Springer Verlag, Bucharest-Berlin, 1970. | MR 0270044 | Zbl 0197.38601

Stečkin S.B. On the approximation properties of sets in normed linear spaces (in Russian), Rev. Math. Pures et Appl. 8 (1963), 5-18. (1963) | MR 0155168

Zukhovickij S.I. On minimal extensions of linear functionals in spaces of continuous functions (in Russian), Izvestija Akad. Nauk SSSR, ser. matem. 21 (1957), 409-422. (1957) | MR 0088702

Werner D. Funktionalanalysis, Springer Verlag, Berlin-Heidelberg-New York, 1995. | MR 1787146 | Zbl 1161.46001