EN
Let V be an n-dimensional real Banach space and let λ(V) denote its absolute projection constant. For any N ∈ N with N ≥ n define
$λₙ^{N} = sup{λ(V): dim(V) = n,V ⊂ l^{(N)}_{∞}}$,
λₙ = sup{λ(V): dim(V) = n}.
A well-known Grünbaum conjecture [Trans. Amer. Math. Soc. 95 (1960)] says that
λ₂ = 4/3.
König 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 Grünbaum conjecture is presented