Subspaces of codimension two with large projection constants

Let V be an n-dimensional real Banach space and let. lambda(V) denote its absolute projection constant. For any N is an element of N, N >= n define lambda(N)(n) = sup{lambda(V): dim(V) = n, V subset of l(infinity)((N))}. The aim of this paper is to determine minimal projections with respect to l(1)-norm as well as with respect to l(infinity)-norm for subspaces given by solutions of certain extremal problems. As an application we show that for any n, N is an element of N, N >= n there exists an n-dimensional subspace V-n subset of l(1)((N)) such that lambda(N)(n) = lambda(V-n,l(1)((N))). Also we calculate relative and absolute projection constants of some subspaces of codimension two in l(1)((N)) and l(infinity)((N)) for N >= 3 being odd natural number. Moreover, we show that for any odd natural number n >= 3, lambda(n+1)(n) < max(x epsilon[0,1]) f(n)(x) <= lambda(n+2)(n), where f(n)(x) = 2n/n+1(1 - x) + 1/2(x - 21-x/n+1 + root(21-x/n+1 - x)(2) + 4(1 - x)x). Also for any n is an element of N x(n) is an element of[0, 1] satisfying f(n)(x(n)) = max(x epsilon[0,1]) fn(x) will be calculated. (C) 2014 Elsevier Inc. All rights reserved.