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Deviation of elements of a Banach space from a system of subspaces

  • S. V. Konyagin
Article

Abstract

We prove that if X is a real Banach space, Y 1Y 2 ⊂ ... is a sequence of strictly embedded closed linear subspaces of X, and d 1d 2 ≥ ... is a nonincreasing sequence converging to zero, then there exists an element xX such that the distance ρ(x, Y n ) from x to Y n satisfies the inequalities d n ρ(x, Y n ) ≤ 8d n for n = 1, 2, ....

Keywords

Hilbert Space Banach Space Positive Integer STEKLOV Institute Number Sequence 
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Copyright information

© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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