Sampling projections in the uniform norm

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 $L_p$.

References in corpus (5)

• A note on sampling recovery of multivariate functions in the uniform norm
• Exponential tractability of $L_2$-approximation with function values
• New lower bounds for the integration of periodic functions
• On the power of iid information for linear approximation
• Sampling discretization of the uniform norm and applications

Cited by in corpus (5)

• On the power of adaption and randomization
• Sampling recovery in $L_2$ and other norms
• Approximation of Functions: Optimal Sampling and Complexity
• Sampling and entropy numbers in the uniform norm
• Minimal projections onto spaces of polynomials on real euclidean spheres