Subprojective Nakano spaces. (English) Zbl 1383.46010
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 F. L. Hernández and 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 \(q<2\).
Reviewer: Elói M. Galego (Sao Paulo)
MSC:
| 46B03 | Isomorphic theory (including renorming) of Banach spaces |
| 46B45 | Banach sequence spaces |
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
Citations:
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