The linearity coefficient of metric projections onto a Chebyshev subspace

DOI10.1134/S0001434609010209zbMath1190.46017OpenAlexW2033002163MaRDI QIDQ1033908

P. A. Borodin

Publication date: 10 November 2009

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434609010209

zbMATH Keywords

Hilbert spaceBanach spacebest approximationLipschitz conditionmetric projectionChebyshev subspacelinearity coefficientquasiorthogonal setUrysohn's Lemma

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Set-valued operators (47H04) Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Banach spaces of continuous, differentiable or analytic functions (46E15)

Related Items (6)

The mapping taking three points of a Banach space to their Steiner point ⋮ The Steiner mapping for three points in Euclidean plane ⋮ Existence of Lipschitz selections of the Steiner map ⋮ Finite-dimensional subspaces of \(L_p\) with Lipschitz metric projection ⋮ An example of a Banach space with non-Lipschitzian metric projection on any straight line ⋮ The linearity coefficient of metric projections onto one-dimensional Chebyshev subspaces of the space \(C\)

Cites Work

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• Chebyshev subspaces of \(L^ 1\) with linear metric projection
• Approximative properties of subspaces in \(c\)-type spaces
• Lipschitz conditions on uniform approximation operators
• Convergence of operators and Korovkin's theorem
• Metric projections onto subspaces of finite codimension
• On nonlinear projections in Banach spaces
• On the complemented subspaces problem
• Characterizations of reflexivity
• The Existence and Unicity of Best Approximations.

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