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Matematicheskie Zametki, 2012, Volume 91, Issue 6, Pages 819–831
DOI: https://doi.org/10.4213/mzm9384 (Mi mzm9384) 		 
This article is cited in 1 scientific paper (total in 1 paper)

$2$-Chebyshev Subspaces in the Spaces $L_1$ and $C$

P. A. Borodin

M. V. Lomonosov Moscow State University
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DOI: https://doi.org/10.4213/mzm9384
Abstract: The $2$-uniqueness subspaces and the finite-dimensional $2$-Chebyshev subspaces of the space $C$ of functions continuous on a Hausdorff compact set and of the space $L_1$ of functions Lebesgue integrable on a set of $\sigma$-finite measure are described. These descriptions are analogs of the well-known Haar and Phelps theorems for ordinary Chebyshev subspaces.
Keywords: Banach space, Hilbert space, $2$-Chebyshev subspace, $2$-uniqueness subspace, $2$-existence subspace, the space $L_1$ of Lebesgue integrable functions.
Received: 29.09.2010
Revised: 12.12.2010
English version:
Mathematical Notes, 2012, Volume 91, Issue 6, Pages 770–781
DOI: https://doi.org/10.1134/S0001434612050239
Bibliographic databases:
Document Type: Article
UDC: 517.982.256
Language: Russian
Citation: P. A. Borodin, “$2$-Chebyshev Subspaces in the Spaces $L_1$ and $C$”, Mat. Zametki, 91:6 (2012), 819–831; Math. Notes, 91:6 (2012), 770–781
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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