V. S. Balaganskii, “Antiproximinal sets in spaces of continuous functions”, Mat. Zametki, 60:5 (1996), 643–657; Math. Notes, 60:5 (1996), 485

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Matematicheskie Zametki, 1996, Volume 60, Issue 5, Pages 643–657
DOI: https://doi.org/10.4213/mzm1878 (Mi mzm1878)

This article is cited in 9 scientific papers (total in 9 papers)

Antiproximinal sets in spaces of continuous functions

V. S. Balaganskii

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Full-text PDF (242 kB) Citations (9)

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DOI: https://doi.org/10.4213/mzm1878

Abstract: Closed convex bounded antiproximinal bodies are constructed in the infinite-dimensional spaces

C (Q)

$C(Q)$ ,

C_{0} (T)

$C_0(T)$ ,

L_{\infty} (S, Σ, μ)

$L_\infty(S,\Sigma,\mu)$ and

B (S)

$B(S)$ , where

Q

$Q$ is a topological space and

T

$T$ is a locally compact Hausdorff space. It is shown that there are no closed bounded antiproximinal sets in Banach spaces with the Radon–Nikodym property.

Received: 20.02.1995

English version:
Mathematical Notes, 1996, Volume 60, Issue 5, Pages 485–494
DOI: https://doi.org/10.1007/BF02309162

Bibliographic databases:

UDC: 517.5

Language: Russian

Citation: V. S. Balaganskii, “Antiproximinal sets in spaces of continuous functions”, Mat. Zametki, 60:5 (1996), 643–657; Math. Notes, 60:5 (1996), 485–494

Citation in format AMSBIB

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\paper Antiproximinal sets in spaces of continuous functions

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\transl

\jour Math. Notes

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\vol 60

\issue 5

\pages 485--494

\crossref{https://doi.org/10.1007/BF02309162}

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Linking options:

https://www.mathnet.ru/eng/mzm1878

https://doi.org/10.4213/mzm1878

https://www.mathnet.ru/eng/mzm/v60/i5/p643

This publication is cited in the following 9 articles:

B. B. Bednov, “The $n$ -antiproximinal sets”, Moscow University Mathematics Bulletin, 70:3 (2015), 130–135
V. S. Balaganskii, “Ob antiproksiminalnykh mnozhestvakh v prostranstve Grotendika”, Tr. IMM UrO RAN, 18, no. 4, 2012, 90–103
V. S. Balaganskii, “On convex closed bounded bodies without farthest points such that the closure of their complement is antiproximinal”, Proc. Steklov Inst. Math. (Suppl.), 277, suppl. 1 (2012), 48–54
V. S. Balaganskii, “On Antiproximal Closed Radially Bounded Convex Sets in the $l_1$ -Space”, Math. Notes, 84:5 (2008), 729–732
V. S. Balaganskii, “Antiproximinal convex bounded sets in the space $c_0(\Gamma)$ equipped with the day norm”, Math. Notes, 79:3 (2006), 299–313
Borwein, JM, “Antiproximinal norms in Banach spaces”, Journal of Approximation Theory, 114:1 (2002), 57
Cobzas, S, “Antiproximinal sets in Banach spaces of continuous vector-valued functions”, Journal of Mathematical Analysis and Applications, 261:2 (2001), 527
V. S. Balaganskii, “Smooth antiproximinal sets”, Math. Notes, 63:3 (1998), 415–418
V. S. Balaganskii, “On nearest and furthest points”, Math. Notes, 63:2 (1998), 250–252

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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