Antiproximinal sets in the Banach space \(C( \omega^k;X)\)

Ştefan Cobzaş

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Ştefan Cobzaş "Babeş Bolyai" University, Cluj-Napoca, Romania

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References

D. Amir, Continuous functions spaces with the separable extension property, Bull. Res, Council Israel 10F (1962), pp. 163-164.

V. S. Balaganskii, An antiproximinal set in a strictly convex space with Fréchet differentiable norm, East J. Approx., 2 (1996), pp. 169-176.

V. S. Balaganskii, Antiproximinal sets in spaces of continuous functions, Matem. Zametki 60 (1996), pp. 643-657 (in Russian), https://doi.org/10.4213/mzm1878

C. Bessaga and A. Pelczynski, Spaces of continuous functions (IV). (On isomorphical classification of spacec C(S)), Studia Math. l9 (1960), pp. 53-62, https://doi.org/10.4064/sm-19-1-53-62

V. L. Chakalov, Extremal lements in some normed spaces, Comptes Rendus Acad. Bulgare des Sciences 36 (1983), pp. 173-176.

S. Cobzaş, Very non-proximinal sets in c₀, Rev. Anal. Numér. Théorie approximation 2 (1973), pp. 137-141 (in Romanian), http://ictp.acad.ro/ranta-ro-72-74

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

S. Cobzaş, Convex antiproximinal sets in the spaces c₀ and c, Matem. Zametki 17 (1975), pp. 449-457 (in Russian).

S. Cobzaş, Antiproximinal sets in Banach spaces of continuous functions, Rev. Anal. Numér.Théorie Approximation 5 (1976), 127-143.

S. Cobzaş, Antiproximinal sets in Banach spaces of c₀-type, Rev. Anal. Numér. Théorie Approximation 7 (1978), pp. 141-145.

S. Cobzaş, Antiproximinal sets in the Banach space c(X), Commentationes Math. Univ. Carolinae 38 (1997), pp. 247-253.

N. Drnford and J. T. Schwartz, Linear Operators I. General Theory, lnterscience, New York 1958, https://doi.org/10.2307/2308567

M. Edelstein and A.C. Thompson, Some results on nearest points and support prperties of convex sets in c₀, Pacific J. Math. 40(1972), pp. 553-560, https://doi.org/10.2140/pjm.1972.40.553

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

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

S. P. Gul'ko and A. V. Os'kin, Isomorphic classification of spaces of continuous functions on totally ordered compacta, Funkc. Analiz i ego Priloženija 9,1 (1975), pp.61-62.

P. R. Halmos, How lo Write Mathemafics, American Mathernatical Society, 1973.

R. B. Holmes, Geometric Functional Analysis and its Applications, Springer Verlag, Berlin-Heidelberg-New York, I975.

V. Klee, Remarks on Nearest Points in Normed Linear Spaces, Proc. Colloq. Convexity, Copenhagen, 1965, pp. 161-176, Copenhagen, 1967.

R. R. Phelps, Subreflexive normed linear spaces, Archiv der Math. 8 (1957), pp. 444-450, https://doi.org/10.1007/bf01898849

R. R. Phelps, Some subreflexive Banach spaces, Archiv. der Math. 10 (1959), pp. 162-169, https://doi.org/10.1007/bf01240781

A.M. Precupanu and T. Precupanu, A characterization of antiproximinal sets, Analele Şt.Univ. Iaşi 33, seria I, Matematica 1987, f.2, pp. 99-106.

Z. Semadeni, Banach spaces of continuous Functions, PWN Warszawa, 1965.

W. Sierpinski, Cardinal and Ordinal Numbers, PWN Warszawa, 1965.

I. Singer, Best Approximation in Normed Linear spaces by Elements of Linear subspaces, Ed. Academiei and Springer Verlag, Bucharest - Berlin 1970, https://doi.org/10.1007/978-3-662-41583-2_4

L.P. Vlasov, Norm attaining functionals on the space C(Q,X), Matem. Zametki 61 (1997), pp. 45-56, https://doi.org/10.4213/mzm1481

S. I. Zukhovickij, On minimal extensions of linear functionals in spaces of continuous functions, Izvestija Akad. Nauk SSSR, Ser.Matem. 21 (1957), pp. 409-422 (in Russian).

D. Wener, Funktionalanalysis, Springer Verlag, Berlin-Heidelberg-New York,1995.