Norming Points and Unique Minimality of Orthogonal Projections

where 1≤ p ≤∞ and μ is normalized Lebesgue measure on (−π,π). LetV be the space of trigonometric polynomials of degree n and let P be the Fourier projection from Lp(−π,π) onto V . It is well known (see [2, 3, 16]) that P is a minimal projection, that is, P has the least norm among all projections from Lp(−π,π) onto V . For p = 1,2 and p =∞, it was proved that P is a unique projection that has this property (see [4, 7]). For the other values of p, the uniqueness of the minimal projection is a wide open question. More generally, let V be a complemented subspace of Lp(μ). Define