Something weaker than the Riesz basis I have some function $f$, real valued and continuous.
I formed functions $\{f_{m,k}, k \in \mathbb{Z}, m>0\}$ such that that $\mathrm{span}\{f_{m,k}, k \in \mathbb{Z}, m>0\}$ is dense in $L_p(R)$.
Now I would like to constract a Riesz basis from $\{f_{m,k}, k \in \mathbb{Z}, m>0\}$, but unfortunately, my $\{f_{m,k}\}$ does not generate a Riesz basis.
I am wondering if there is some weaker/stronger structure than the Riesz basis, such that $\{f_{m,k}, k \in \mathbb{Z}, m>0\}$ can possibly generate?
Thank you.

The term you're looking for is probably Schauder basis, altough for that you also need some independence properties (as usual with bases).
