Sampling projections in the uniform norm

We show that there are sampling projections on arbitrary n-dimensional subspaces of B(D) with at most 2n samples and norm of order √(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.