Equal-norm parseval K-frames in Hilbert Spaces

TL;DR

This paper investigates equal-norm Parseval K-frames in Hilbert spaces, establishing their extension, correspondence with subspaces, and dual frame construction, which enhances understanding of their structure and applications.

Contribution

It introduces new results on extending finite equal-norm sets to K-frames, links Parseval K-frames with subspace sets, and constructs equal-norm dual K-frames.

Findings

Finite equal-norm sets can be extended to equal-norm K-frames.

A correspondence exists between Parseval K-frames and closed subspaces.

A method for constructing equal-norm dual K-frames is provided.

Abstract

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.