A proof of the Grünbaum conjecture

Bruce L. Chalmers, and Grzegorz Lewicki. "A proof of the Grünbaum conjecture." Studia Mathematica 200.2 (2010): 103-129. <http://eudml.org/doc/285668>.

@article{BruceL2010,
abstract = {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 = supλ(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},
author = {Bruce L. Chalmers, Grzegorz Lewicki},
journal = {Studia Mathematica},
keywords = {projection constant},
language = {eng},
number = {2},
pages = {103-129},
title = {A proof of the Grünbaum conjecture},
url = {http://eudml.org/doc/285668},
volume = {200},
year = {2010},
}

TY - JOUR
AU - Bruce L. Chalmers
AU - Grzegorz Lewicki
TI - A proof of the Grünbaum conjecture
JO - Studia Mathematica
PY - 2010
VL - 200
IS - 2
SP - 103
EP - 129
AB - 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 = supλ(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
LA - eng
KW - projection constant
UR - http://eudml.org/doc/285668
ER -