Q-duals and Q-approximate duals of g-frames in Hilbert spaces. (26th April 2023)

• Record Type: Journal Article
• Authors: Xiao, Xiangchun; Zhao, Guoping; Zhou, Guorong
• Is Part Of: Numerical functional analysis and optimization. Volume 44:Number 6(2023)
• Page Start: 510
• Page End: 528
• Publication Date: 2023-04-26
• Subjects: Approximate dual -- G-frame -- Q-dual -- synthesis operator; 42C15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2023.2184383
• Languages: English
• ISSNs: 0163-0563

Abstract

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.