This is an announcement for the paper "An uniform estimate of the relative projection constant" by Tomasz Kobos.

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 $||P|| > 1 + \left (2 \left ( n + 3 \right )^{2} \right )^{-100(n+3)^2}$ holds. This gives a non-trivial lower bound in a variation of problem proposed by Bosznay and Garay in $1986$.

Archive classification: math.FA

Mathematics Subject Classification: 47A58, 41A65, 47A30, 52A21

Remarks: 15 pages

Submitted from: tkobos@wp.pl

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1508.03518

or

http://arXiv.org/abs/1508.03518