Extending operators into Lindenstrauss spaces
\textit{J.\,Lindenstrauss} and \textit{A.\,Pełczyński} [J.~Funct.\ Anal.\ 8, 225--249 (1971; Zbl 0224.46041)] proved that every \(C(K)\)-valued operator from a subspace of \(c_{0}\) can be extended to the whole \(c_{0}\). In that paper,they also remarked that the same result is valid when replacing \(C(K)\)-spaces by ``isometric \(L_{1}\)-preduals'', henceforth called Lindenstrauss spaces. As its title suggests, the paper under review deals with extensions of operators into Lindenstrauss spaces. Among several deep results, the authors extend Lindenstrauss--Pełczyński's result to the nonseparable case and provide new constructions in which the extension of operators into Lindenstrauss spaces exists; for example, it is shown that the Bourgain--Pisier construction of \(\mathcal{L}_{\infty}\)-spaces [\textit{J.\,Bourgain} and \textit{G.\,Pisier}, Bol.\ Soc.\ Bras.\ Mat.\ 14, No.\,2, 109--123 (1983; Zbl 0586.46011)] is one of those.
scientific article; zbMATH DE number 5508731
scientific article