Q-duals and Q-approximate duals of g-frames in Hilbert spaces. (26th April 2023) - Xiao, Xiangchun; Zhao, Guoping; Zhou, Guorong
Abstract: In this paper we mainly discuss the properties of Q -duals and Q -approximate duals of g-frames in Hilbert spaces. Given Λ j j ∈ J and Θ j j ∈ J being a pair of Q -dual, Γ j j ∈ J being some kind of perturbed sequence of Θ j j ∈ J, in general Λ j j ∈ J is not a Q -approximate dual of Γ j j ∈ J . We then give four different kinds of perturbed conditions such that Λ j j ∈ J and Γ j j ∈ J, a perturbed sequence of Θ j j ∈ J, are possible to be a pair of Q -approximate dual. We also provide several different methods to construct Q -duals and Q -approximate duals of g-frames. Finally, we give two equivalent characterizations of Q -duals and Q -approximate duals by using the associated induced sequences.