Generalized frames and controlled operators in Hilbert space

Abstract: Controlled frames and g-frames were considered recently as generalizations of frames in Hilbert spaces. In this paper we generalize some of the known results in frame theory to controlled g-frames. We obtain some new properties of controlled g-frames and obtain new controlled g-frames by considering controlled g-frames for its components. And we obtain some new resolutions of the identity. Furthermore, we study the stabilities of controlled g-frames under small perturbations.