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

Abstract

This paper addresses controlled g-frames which are extensions of g-frames and controlled frames. Firstly, we discuss the characterization of controlled g-frames, obtain some equivalent conditions of them. Then, we introduce the concept of controlled dual g-frames and controlled dual g-frames operator, get some properties of them. Finally, we characterize all controlled dual g-frames of a controlled generalized frame.2010 MS Classification: 42C15, 42A38