Constructions of K-g-fusion and their dual in Hilbert spaces

Abstract

Frames for operators or K-frames were recently considered by Găvruța (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 also known as K-g-fusion frames and we get some results for characterization of these frames. We further discuss dual and Q-dual 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.