L-space links and link Floer homology

We define a subfamily of L-space links, called special L-space links, and we prove that, for such links, many properties which holds for L-space knots are satisfied. In particular, we are able to show that special L-space links are fibered and strongly quasi-positive. This is achieved by using the fact that the Ozsváth-Szabó τ invariant, in its link version, detects fibered strongly quasi-positive links. Moreover, we can prove that this subfamily includes the family of algebraic links.