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.