Subprojective Nakano spaces
Recall that a Banach space \(X\) is said to be subprojective if every infinite-dimensional subspace of \(X\) has an infinite-dimensional subspace which is complemented in \(X\). The authors prove that separable Nakano sequence spaces \(\ell_{(p_{n})}\) are subprojective. Moreover, by using the results of \textit{F. L. Hernández} and \textit{C. Ruiz} [J. Math. Anal. Appl. 389, No. 2, 899--907 (2012; Zbl 1257.46012)] on subspaces of separable Nakano function spaces, they show that \(L^{p(\cdot)}\) is subprojective if and only if it does not contain a subspace isomorphic to \(l_{q}\) with \(q<2\).
scientific article; zbMATH DE number 6802316
scientific article