Operator characterizations and constructions of continuous g-frames in Hilbert spaces

Abstract

ABSTRACT This paper addresses continuous g-frames which are extensions of g-frames and continuous frames. First, we study the dual of continuous g-frames, which are critical components in reconstructions. We give the characterizations of dual continuous g-frames in terms of continuous g-preframe operators. The formulae of dual continuous g-frames for a given continuous g-frame are given. Second, we discuss the constructions of continuous g-frames in Hilbert spaces. We mainly consider the constructions of new continuous g-frames from known ones under certain conditions, which generalize the corresponding results on g-frames. In particular, we obtain a necessary and sufficient condition for the finite sum of continuous g-frames to be a continuous g-frame.