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.

Keywords: Frames; $K$-frames; scalable $K$-frames.

MSC: 42C15, 47A63

DOI: 10.57016/MV-7942HXLN

Pages:  225$-$234     

Volume  75 ,  Issue  4 ,  2023