Weak Chebyshev subspaces and 𝐴-subspaces of 𝐶[𝑎,𝑏]

Abstract

In this paper we show some very interesting properties of weak Chebyshev subspaces and use them to simplify Pinkus’s characterization of A A subspaces of C [ a , b ] C[a,b] . As a consequence we obtain that if the metric projection P G {P_G} from C [ a , b ] C[a,b] onto a finite-dimensional subspace G G has a continuous selection and elements of G G have no common zeros on ( a , b ) (a,b) , then G G is an A A -subspace.