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JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2012 Volume 91, Issue 6, Pages 819–831 (Mi mzm9384)

This article is cited in 1 paper

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

P. A. Borodin

M. V. Lomonosov Moscow State University

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.

UDC: 517.982.256

Received: 29.09.2010
Revised: 12.12.2010

DOI: 10.4213/mzm9384


 English version:
Mathematical Notes, 2012, 91:6, 770–781

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