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Morris, Peter D.

Chebyshev subspaces of \(L^ 1\) with linear metric projection. (English) Zbl 0466.41015

J. Approximation Theory 29, 231-234 (1980).
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Cited in 7 Documents

MSC:

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A50 Best approximation, Chebyshev systems
41A52 Uniqueness of best approximation

Keywords:

L-1-approximation; Chebyshev subspaces
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References:

[1] Ahieser, N. I.; Krein, M. G., Some Questions in the Theory of Moments, (Transl. Math. Monographs, Vol. 2 (1962), Amer. Math. Soc: Amer. Math. Soc Providence, R.I) · Zbl 0117.32702
[2] Cheney, E. W.; Wulbert, D. E., The existence and unicity of best approximations, Math. Scand., 24, 113-140 (1969) · Zbl 0186.18701
[3] Kahane, J.-P, Projection métrique de \(L^1(T)\) sur des sous-espaces fermés invariants par translation, (Oberwolfach Proc. ISNM, 20 (1971)), 302-309 · Zbl 0253.43004
[4] Mazur, S., Über konvexe Mengen in linearen normierten Räumen, Studia Math., 4, 70-84 (1933) · Zbl 0008.31603
[5] Morris, P. D., Metric projections onto subspaces of finite codimension, Duke Math. J., 35, 799-808 (1968) · Zbl 0167.42301
[6] Phelps, R. R., Uniqueness of Hahn-Banach extensions and unique best approximations, Trans. Amer. Math. Soc., 95, 238-255 (1960) · Zbl 0096.31102
[7] Phelps, R. R., Čebyšev subspaces of finite dimension in \(L_1\), (Proc. Amer. Math. Soc., 17 (1966)), 646-652 · Zbl 0156.36502
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