Scalable g-frame in Hilbert spaces

Tight frames and g-frames are extremely useful in applications. A scalable frame was recentlyintroduced as a frame with the property of generating a tight frame by rescaling its frame vectors. In thispaper, we generalize this concept to g-frames, introduce scalable g-frames, obtain some characterizationsfor them, and demonstrate that scalability is stable under unitary operators and isomorophisms betweentwo Hilbert spaces. In addition, we consider Paley-Wiener perturbations of g-frames and achieve someresults regarding the preservation of their g-frame property.