A proof of the Grunbaum conjecture

作者：Chalmers Bruce L^*; Lewicki Grzegorz

来源：Studia Mathematica, 2010, 200(2): 103-129.

DOI：10.4064/sm200-2-1

• absolute projection constant
• minimal projection

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.

• 出版日期2010