Controlled g-frames and dual g-frames in Hilbert spaces

Abstract

Abstract As generalizations of g-frames and controlled frames, the theory of controlled g-frames has been deeply studied. This paper addresses the controlled g-frames and dual g-frames in Hilbert spaces. We first present some equivalent characterizations of controlled g-frames. Then, we introduce the concepts of controlled dual g-frames and controlled dual g-frames operator, get some properties of them. Finally, we obtain some characterizations of the controlled dual g-frames for a given controlled g-frame by the method of operator theory.

Keywords

• G-frames
• Controlled g-frames
• Controlled dual g-frames