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The Linearity of Metric Projection Operator for Subspaces of Lp Spaces / Druzhinin Yu.Yu. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. № 1. P. 30-36 [Moscow Univ. Math. Bulletin. Vol. 65, No 1, 2010. P. 28-33]. Let Y be a Chebyshev subspace of a Banach space X. Then the single-valued metric projection operator PY: X→Y taking each x∈X to the nearest element y∈Y is well defined. Let M be an arbitrary set and μ be a σ-finite measure on some σ-algebra Σ of subsets of M. We give a description of Chebyshev subspaces Y⊂Lp(M,Σ,μ) with a finite dimension and a finite codimension which the operator PY is linear for.
Key words: metric projection, Chebyshev subspace, quasiorthogonal set,
linearity criterion.
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