Subprojective Nakano spaces

A Banach space X is subprojective if every infinite-dimensional subspace of X has a subspace which is complemented in X. We prove that separable Nakano sequence spaces ℓ(pn) are subprojective. Subprojectivity is also characterized in separable Nakano function spaces Lp(⋅)(0,1) and Lp(⋅)(0,∞).