A proof of the Grunbaum conjecture

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 with N >= n define lambda(N)(n) = sup{lambda(V) : dim(V) = n, V subset of l(infinity)((N))}, lambda(n) = sup{lambda(V) : dim(V) = n}. A well-known Grunbaum conjecture [Trans. Amer. Math. Soc. 95 (1960)] says that lambda(2) = 4/3. Konig and Tomczak-Jaegermann [J. Funct. Anal. 119 (1994)] made an attempt to prove this conjecture. Unfortunately, their Proposition 3.1, used in the proof, is incorrect. In this paper a complete proof of the Griinbaum conjecture is presented.