Sampling projections in the uniform norm

Abstract

We show that there are sampling projections onto arbitrary n-dimensional subspaces of $B\left(D\right)$ with at most 2n samples and norm of order $\sqrt{n}$, where $B\left(D\right)$ is the space of bounded functions on a set D. This gives a more explicit form of the Kadets-Snobar theorem for the uniform norm. We discuss consequences for optimal recovery in $L_p$.