Convex antiproximinal sets in spaces \(c_0\) and \(c\). (English. Russian original) Zbl 0327.41030
Math. Notes 17, 263-268 (1975); translation from Mat. Zametki 17, 449-457 (1975).
MSC:
| 41A65 | Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) |
| 46B99 | Normed linear spaces and Banach spaces; Banach lattices |
| 41A50 | Best approximation, Chebyshev systems |
References:
| [1] | R. R. Holmes, A Course on Optimization and Best Approximation, Lecture Notes in Math., No. 257, Springer-Verlag (1972). · Zbl 0235.41016 |
| [2] | V. Klee, ?Remarks on nearest points in normed linear spaces,? Proc. Colloq. Convexity (Copenhagen, 1965), Copenhagen (1967), pp. 168-176. |
| [3] | M. Edelstein, ?A note on nearest points,? Quart. J. Math.,21, No. 84, 403-406 (1970). · Zbl 0201.44505 · doi:10.1093/qmath/21.4.403 |
| [4] | M. Edelstein and A. C. Thompson, ?Some results on nearest points and support properties of convex sets in c0,? Pacific J. Math.,40, No. 3, 553-560 (1972). · Zbl 0202.39503 |
| [5] | S. Banach, Théorie des Opérations Linéaires, Warszawa (1932). |
| [6] | N. Dunford and J. T. Schwartz, Linear Operators, Part I: General Theory, Wiley (1959). · Zbl 0084.10402 |
| [7] | V. D. Mil’man, ?Geometric theory of Banach spaces, I. Theory of base and minimal systems,? Usp. Matem. Nauk,25, No. 3, 113-171 (1970). |
| [8] | S. I. Zukhovitskii, ?On minimal extensions of linear functionals in the space of continuous functions,? Izv. Akad. Nauk SSSR, Ser. Matem.,21, No. 3, 409-422 (1957). |
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