Three-dimensional subspace of \(l^{(5)}_\infty\) with maximal projection constant (Q1029321)

The title of this paper tells only half the story. In a remarkable tour de force, the aforementioned constant is calculated exactly. By itself, this may not seem so interesting. However, it shows that Proposition 3.1 of \textit{H.\,König} and \textit{N.\,Tomczak-Jaegermann} [J.~Funct.\ Anal.\ 119, No.\,2, 253--280 (1994; Zbl 0818.46015)] is not correct; Theorem 2.2 of the present paper is essentially a corrected version of that. The proof of Grünbaum's conjecture (that every 2-dimensional space has projection constant not exceeding 4/3) given in [loc. cit.] depended on Proposition 3.1, and is therefore not complete. In an extension of the paper under review [``A~proof of the Grünbaum conjecture'', Stud.\ Math.\ 200, No.\,2, 103--129 (2010; Zbl 1255.46005)], the authors give a complete argument for that problem as well.