Some Identities and Inequalities for Hilbert-Schmidt Frames

TL;DR

This paper introduces new identities and inequalities for Hilbert-Schmidt frames, extending and enhancing previous results to deepen understanding of their mathematical properties.

Contribution

It presents novel Parseval type identities and inequalities for Hilbert-Schmidt frames, generalizing prior work by Balan et al. and G4vru4a.

Findings

New Parseval type identities for Hilbert-Schmidt frames

Surprising inequalities that improve existing bounds

Generalizations of previous results by Balan et al. and G4vru4a

Abstract

In this paper we establish Parseval type identities and surprising new inequalities for Hilbert-Schmidt frames. Our results generalize and improve the remarkable results which have been obtained by Balan et al. and G{\u{a}}vru{\c{t}}a.