An extension property of the Bourgain-Pisier construction
Extensions of operators, especially with preservation of the norm, lie at the heart of functional analysis. This paper adds a significant class of examples. If \(X\) is a separable Banach space, \(\mu\geq1\), and \(Y=\mathcal{L}_{\infty,\mu+\varepsilon}(X)\) is a Bourgain-Pisier space associated with \(X\), then every linear operator from \(X\) into any \(\mathcal{L}_{\infty,\mu}\) space admits a norm preserving extension to \(Y\). This is really nontrivial since, for example, \(Y/X\) has the Schur property.
scientific article; zbMATH DE number 6203782