New Constructions of Scalable K-frames

The invariance of frames and their extensions under the operator perturbation is one of the most important problems in frame theory.In this paper, we focus on the stabilities of scalable K-frames under the operator perturbation and thenwe construct new scalable K-frames for Hilbert spaces by some operator theory tools.More precisely, we investigate several sufficient and/or conditionsof the operator perturbation for a scalable K-frame by using certain operators with specific properties.Finally, since the finite sum of scalable K-frames may not be a scalable K-frames forthe Hilbert space, we demonstrate that under some special conditions, the sum of two scalable K-frames remains a scalable K-frame.

کلیدواژه ها:

K-frames ، scalable K-frames ، Operator perturbation