Scalability of Generalized Frames for Operators

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 .