A note on best selection of quasi Descartes systems

Abstract

Let \(\{u_0, \dots, u_n\}\) be a quasi Descartes system of \(C[a, b]\) and \(p\) a positive number with \(1 < p < \infty\) or \(\infty\). In this note, we search for an \(m (\leqq n)\) dimensional subspace that possesses the least distance from \(u_n\) among all \(m (\leqq n)\) dimensional subspaces of \({\rm Span}\{ u_0, \ldots, u_{n-1}\}\).