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arXiv · 1508.03518

A uniform estimate of the relative projection constant

Tomasz Kobos
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Abstract

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 $\ell_{2p}^m$ space and $Y \subset X$ is an arbitrary hyperplane. As a consequence, we establish that for every integer $n \geq 4$ there exists an $n$-dimensional normed space $X$ such that for an every hyperplane $Y$ and every projection $P:X \to Y$ the inequality $||P|| > 1 + \left (8 \left ( n + 3 \right )^{5} \right )^{-30(n+3)^2}$ holds. This gives a non-trivial lower bound in a variation of problem proposed by Bosznay and Garay in $1986$.

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Tomasz Kobos. 2015-08-14. A uniform estimate of the relative projection constant. https://arxiv.org/abs/1508.03518

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