A Schauder basis for $$L_2$$ consisting of non-negative functions

We prove that \(L_2(\mathbb {R})\) contains a Schauder basis of non-negative functions. Similarly, for all \(1<p<\infty \), \(L_{p}(\mathbb basic sequence functions such \(L_p(\mathbb embeds into the closed span sequence. as well if X is separable Banach space with bounded approximation property, then any set in dense quasi-basis (Schauder frame) X.