Subspaces of codimension two with large projection constants

Let V be an n-dimensional real Banach space and let λ(V) denote its absolute projection constant. For any N∈N, N≥n defineλnN=sup⁡{λ(V):dim⁡(V)=n,V⊂l∞(N)}. The aim of this paper is to determine minimal projections with respect to l1-norm as well as with respect to l∞-norm for subspaces given by solutions of certain extremal problems. As an application we show that for any n,N∈N, N≥n there exists an n-dimensional subspace Vn⊂l1(N) such thatλnN=λ(Vn,l1(N)). Also we calculate relative and absolute projection constants of some subspaces of codimension two in l1(N) and l∞(N) for N≥3 being odd natural number. Moreover, we show that for any odd natural number n≥3,λnn+1