Minimal projections onto hyperplanes in ℓpn

The purpose of this paper is to find the relative projection constant of ker{1}={x:∑i=1nxi=0} in ℓpn for an arbitrary nn (see Theorem 2.28). This extends a result of L. Skrzypek obtained for n=3,4n=3,4. We also improve on the formula for the relative projection constant onto hyperplanes in Lp[0,1]Lp[0,1] obtained by C. Franchetti (see Theorem 2.21) and reprove a result of S. Rolewicz (see Corollary 2.11).