A uniform estimate of the relative projection constant

2015/08/14 by Kobos, Tomasz · 1 citation
#41A65 #47A30 #47A58 #52A21 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1508.03518

Abstract

The main goal of the paper is to provide a quantitative lower bound greater than 1 for the relative projection constant λ(Y, X), where X is a subspace of ℓ_2p^m space and Y ⊂ 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 ||P|| > 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 and Garay in 1986.

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