2-Chebyshev subspaces in the spaces L1 and C

被引：0
作者：
P. A. Borodin
机构：
[1] Moscow State University,
来源：
Mathematical Notes | 2012年 / 91卷
关键词：
Banach space; Hilbert space; 2-Chebyshev subspace; 2-uniqueness subspace; 2-existence subspace; the space L; of Lebesgue integrable functions;
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学科分类号：
摘要：
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 L1 of functions Lebesgue integrable on a set of σ-finite measure are described. These descriptions are analogs of the well-known Haar and Phelps theorems for ordinary Chebyshev subspaces.
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页码：770 / 781
页数：11
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共 14 条
  • [1] Efimov N. V.(1958)Some properties of Chebyshev sets Dokl. Akad. Nauk SSSR 118 17-19
  • [2] Stechkin S. B.(1996)The problem of convexity of Chebyshev sets Uspekhi Mat. Nauk 51 125-188
  • [3] Balaganskii V. S.(1965)On an extremal problem in a linear normed space Sibirsk. Mat. Zh. 6 711-714
  • [4] Vlasov L. P.(1969)The existence and unicity of best approximations Math. Scand. 24 113-140
  • [5] Rubinshtein G. Sh.(1963)Čebyšev subspaces of finite codimension in Pacific J.Math. 13 647-655
  • [6] Cheney E. W.(1917)( Math. Ann. 78 294-311
  • [7] Wulbert D. E.(1956)) Proc. Amer. Math. Soc. 7 609-615
  • [8] Phelps R. R.(1966)Die Minkowskische Geometrie und die Annäherung an stetige Funktionen Proc. Amer. Math. Soc. 17 646-652
  • [9] Haar A.(1960)On Haar’s theorem concerning Chebychev approximation problems having unique solutions Trans.Amer.Math. Soc. 95 238-255
  • [10] Mairhuber J. C.(1980)Čebyšev subspaces of finite dimension in J. Approx. Theory 29 231-234
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