K-Frames from Finite Extensions

In this paper, we study finite extensions of Bessel sequences to K-frames in a separable Hilbert space H. Precisely, we give some necessary and sufficient conditions for a Bessel sequence such that it can be expanded to a K-frame and a Parseval K-frame by adding finite number of elements in H. Also we show that under some conditions, a frame can be extended to a Parseval K-frame.

Automated summary

In this paper, we investigate finite extensions of Bessel sequences to K-frames in a separable Hilbert space H. We provide necessary and sufficient conditions for a Bessel sequence to be expanded to a K-frame and a Parseval K-frame by adding a finite number of elements in H. Additionally, we demonstrate that a frame can be extended to a Parseval K-frame under certain conditions.