Questions in linear recurrence II: Lineability properties

Motivated by the recently introduced notion of quasi-rigidity we study, for a continuous linear operator T acting on an F-space X and for an appropriated Furstenberg family F ⊂ P(N₀) F ⊂ P ( N 0 ) , when the respective set of F F -recurrent vectors FRec(T) F Rec ( T ) is lineable or even dense lineable. To this end we recall and generalize some basic but useful results on how homomorphisms, quasi-conjugacies and commutants behave with respect to Furstenberg families in pointwise recurrence.