Abstract:

In this paper we have given the definitions of 2K- frames and 2K-g-frames, with the help of this we have proved, if  is K-frame and  is a 2K-frame then  is a K-frame for H and also, we give a condition on sum of 2K-g frames is a K-g frame for Hilbert space. Some results on 2K-frames were presented by using an injective closed range operator .                 Mathematics Subject Classification (2010): 42C15.

Keywords: frame, k-frame, g-frame, 2k-frame, 2-kg-frames.