This article is cited in 1 paper

Operator of best approximation on finite-dimensional subspaces

V. I. Berdyshev

Institute of Mathematics and Mechanics, Ural Science Center, Academy of Sciences of the USSR

Abstract: The modulus of continuity of the operator of best approximation on a subspace tends towards zero uniformly on the class of all subspaces of an n-dimensional space only if the unit ball of the space contains no extremal subsets of dimensionality $k$ ($0<k<n-1$).

UDC: 517.5

Received: 21.01.1974

 English version: Mathematical Notes, 1974, 16:3, 888–893

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