The Pólya algorithm on tubular sets

AbstractSuppose K is a compact convex subset of Rn. If for every x∈Rn, the net of best lp-approximants, from K, of x converges to the strict uniform approximant as p → ∞, we call K a strict Pólya set. Two conditions which guarantee that K is a strict Pólya set have recently been published. The present paper shows that these conditions are essentially equivalent, demonstrates that all closed strictly convex sets satisfy the conditions, and describes a set which is strict Pólya but does not satisfy the conditions