Sampling projections in the uniform norm

David Krieg; Kateryna Pozharska; Mario Ullrich; Tino Ullrich

doi:10.1016/j.jmaa.2025.129873

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arXiv · 2401.02220

Sampling projections in the uniform norm

David Krieg·Kateryna Pozharska·Mario Ullrich·Tino Ullrich

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Abstract

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

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David Krieg, Kateryna Pozharska, Mario Ullrich, Tino Ullrich. 2024-01-04. Sampling projections in the uniform norm. https://doi.org/10.1016/j.jmaa.2025.129873

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