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.