Dual and approximately dual Hilbert-Schmidt frames in Hilbert spaces (Q1743208)

The author introduces the concept of approximately dual Hilbert-Schmidt frames in Hilbert spaces. He establishes the relations between approximately dual Hilbert-Schmidt frames and dual Hilbert-Schmidt frames, and between approximately dual Hilbert-Schmidt frames and approximately dual frames. Also, he obtains a method to construct approximately dual Hilbert-Schmidt frames. Finally, the author presents a perturbation result and discusses the stability of the perturbation of dual Hilbert-Schmidt frames and approximately dual Hilbert-Schmidt frames.