Currently displaying 1 – 3 of 3

Showing per page

Order by Relevance | Title | Year of publication

Two-dimensional real symmetric spaces with maximal projection constant

Bruce ChalmersGrzegorz Lewicki — 2000

Annales Polonici Mathematici

Let V be a two-dimensional real symmetric space with unit ball having 8n extreme points. Let λ(V) denote the absolute projection constant of V. We show that λ ( V ) λ ( V n ) where V n is the space whose ball is a regular 8n-polygon. Also we reprove a result of [1] and [5] which states that 4 / π = λ ( l ( 2 ) ) λ ( V ) for any two-dimensional real symmetric space V.

A proof of the Grünbaum conjecture

Bruce L. ChalmersGrzegorz Lewicki — 2010

Studia Mathematica

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 λ N = s u p λ ( V ) : d i m ( 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

Page 1

Download Results (CSV)