A uniform estimate of the relative projection constant

JOURNAL OF APPROXIMATION THEORY

卷:225

Article

Kobos, Tomasz¹ 

[1] Jagiellonian Univ, Fac Math & Comp Sci, Lojasiewicza 6, PL-30348 Krakow, Poland

关键词: Minimal projection;    Finite-dimensional normed space;   

DOI  :  10.1016/j.jat.2017.09.006

来源: Elsevier

【 摘 要 】

The main goal of the paper is to provide a quantitative lower bound greater than 1 for the relative projection constant lambda(Y, X), where X is a subspace of l(2p)(m) space and Y subset of X is an arbitrary hyperplane. As a consequence, we establish that for every integer n >= 4 there exists an n-dimensional normed space X such that for an every hyperplane Y and every projection P : X -> Y the inequality parallel to P parallel to > 1 + (8(n+3)(5))(-30(n+3)2) holds. This gives a non-trivial lower bound in a variation of problem proposed by Bosznay an Garay in 1986. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free