A proof of the Grünbaum conjecture

• Autorzy: Bruce L. Chalmers , Grzegorz Lewicki
• Języki publikacji: EN

Abstrakty

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

Kategorie tematyczne

• 47A30: Norms (inequalities, more than one norm, etc.)
• 47A58: Operator approximation theory
• 46A22: Theorems of Hahn-Banach type; extension and lifting of functionals and operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2010
• Tom: 200
• Numer: 2
• Strony: 103-129

Daty

wydano

2010

Twórcy

autor

Bruce L. Chalmers

• Department of Mathematics, University of California, Riverside, CA 92521, U.S.A.

autor

Grzegorz Lewicki

• Institute of Mathematics, Jagiellonian University, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/sm200-2-1