Construction of k-g-fusion frames and their duals in Hilbert spaces

Abstract

Frames for operators or k-frames were recently considered by Gavruta (2012) in connection with atomic systems. Also generalized frames are important frames in the Hilbert space of bounded linear operators. Fusion frames, which are a special case of generalized frames have various applications. This paper introduces the concept of generalized fusion frames for operators aka k-g-fusion frames and we get some results for characterization of these frames. We further discuss on duals and Q-duals in connection with k-g-fusion frames. Also we obtain some useful identities for these frames. We also give several methods to construct k-g-fusion frames. The results of this paper can be used in sampling theory which are developed by g-frames and especially fusion frames. In the end, we discuss the stability of a more general perturbation for k-g-fusion frames.