SOME RESULTS ON SCALABLE K-FRAMES

Abstract

We investigate the scalability of $K$-frames and derive a characterization for scalable $K$-frames. We investigate whether or not a particular $K$-frame is scalable, as well as the existence and uniqueness of scalings. Using the concept of trace of an operator, we analyse the possible scalings, if a given $K$-frame is scalable. In ${\mathbb{C}}^n$, we look at the scalability of $K$-frames independently.