  In this paper, we focus on frames of operators or K-frames on Hilbert spaces
in Parseval cases. Since equal-norm tight frames play important roles for
robust data transmission, we aim to study this topics on Parseval K-frames. We
will show that each finite set of equal-norms of vectors can be extended to an
equal-norm K-frame. Also, we present a correspondence between Parseval K-frames
and the set of all closed subspaces of a finite Hilbert space. Finally, a
construction of equal-norm dual K-frames will be introduced.

Functional Analysis