Hilbert–Schmidt Frames: Duality, Weaving and Stability

In this paper, we give some sufficient conditions under which perturbations preserve Hilbert-Schmidt frames. Also show that the canonical dual of a perturbed Hilbert-Schmidt frame is a perturbation of the canonical dual (alternative dual respectively) of the original Hilbert-Schmidt frame and discuss best approximation in the set of all dual Hilbert-Schmidt frames. Next, we apply the woven principle to Hilbert-Schmidt frames and study the stability of weaving Hilbert-Schmidt frames under perturbations. Finally, we present sufficient conditions under which perturbations preserve weaving Hilbert-Schmidt frames and weaving dual Hilbert-Schmidt frames.

Keywords:

Hilbert-Schmidt frames , Weaving frames , Dual frames , Perturbation