Equal-norm Parseval K-frames in Hilbert spaces with a new inequality

Abstract

Abstract The focus of this paper is mainly on the frames of operators or K-frames on Hilbert spaces in Parseval cases. Since equal-norm tight frames play an important role for transmitting robust data, we aim to study this topic on Parseval K-frames. We find that each finite set of equal-norm of vectors can be extended to an equal-norm K-frame. We also find a correspondence between Parseval K-frames and the set of all closed subspaces of a finite Hilbert space. Furthermore, we provide a construction of dual equal-norm K-frames.

Keywords

• Parseval frames
• K-frames
• K-dual frames