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A proof of the Grünbaum conjecture

Bruce L. Chalmers, Grzegorz 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

À propos d'une question posée par V. Klee

Jean-Claude Dupin, Gérard Coquet (1974)

Annales de l'institut Fourier

Nous répondons par la négative à une question posée par Klee (Mathematical Note no 599, Boeing Scientific Research Laboratories, p.29).

A quantitative version of Krein's theorem.

M. Fabian, P. Hájek, V. Montesinos, V. Zizler (2005)

Revista Matemática Iberoamericana

A quantitative version of Krein's Theorem on convex hulls of weak compact sets is proved. Some applications to weakly compactly generated Banach spaces are given.

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