Minimal projections onto two dimensional subspaces of \(l_ \infty^{(4)}\)
Let \((X,|\cdot|)\) be a normed linear space. Let \(Y\subseteq X\), and let \(F\) be some collection of operators from \(X\) into \(Y\). The general problem related to this paper is that of identifying the operators in \(F\) of minimal norm. For example, classically important results include the cases when \(X= C[-1,1]\) or \(C_{2\pi}\), \(Y\) is respectively the polynomials of degree \(n\) or the trigonometric polynomials of degree \(n\), and \(F\) is respectively the interpolating projections or the set of all projections. This paper identifies the minimal projections from the 4-dimensional space with the maximum norm onto 2-dimensional subspaces. The statement of the theorem is very long and technical. The paper also determines when the minimal projection is unique.
scientific article; zbMATH DE number 980682