Approximation of the Inverse Frame Operator and Stability of Hilbert$-$Schmidt Frames

Abstract

In this paper, we study the Hilbert$-$Schmidt frame (HS-frame) theory for separable Hilbert spaces. We first present some characterizations of HS-frames and prove that HS-frames share many important properties with frames. Then, we show how the inverse of the HS-frame operator can be approximated using finite-dimensional methods. Finally, we present a classical perturbation result and prove that HS-frames are stable under small perturbations.

22 pages

References in corpus (2)

• Some Identities and Inequalities for Hilbert-Schmidt Frames
• Behavior of Gabor frame operators on Wiener amalgam spaces

Cited by in corpus (1)

• Semi-continuous g-frames in Hilbert spaces