Scalability of Generalized Frames for Operators

Abstract

In this paper, the Parseval K-g-frames are constructed from a given K-g-frame by scaling the elements of the K-g-frame with the help of diagonal operators, and these frames are named scalable K-g-frames. Also, we prove some properties of scalable K-g-frames and construct new scalable K-g-frames from a given K-g-frame. The necessary and sufficient conditions for a K-g-frame to be scalable are given. Further, equivalent conditions for the scalability of K-g-frames and the K-frames induced by K-g-frames are obtained. Finally, it is shown that the direct sum of two scalable K-g-frames is again a scalable K-g-frame for some suitable bounded linear operator K.