On sum and stability of g-frames in Hilbert spaces. Issue 8 (3rd August 2018)

• Record Type: Journal Article
• Authors: Li, Dongwei; Leng, Jinsong; Huang, Tingzhu; Sun, Guomin
• Is Part Of: Linear & multilinear algebra. Volume 66:Issue 8(2018)
• Page Start: 1578
• Page End: 1592
• Publication Date: 2018-08-03
• Subjects: Frame -- g-frame -- tight g-frame -- stability; 42C15 -- 41A58; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2017.1364338
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract: In this paper, we give some new results on sum and stability of g-frames in Hilbert spaces. Since the finite sum of g-frames may not be a g-frame for the Hilbert space, we give a necessary and sufficient condition and some sufficient conditions for the finite sum of g-frames to be a g-frame. We also show that every g-sequence in Hilbert space can be expanded to a tight g-frame by adding a linear bounded operator. Moreover, we obtain some sufficient conditions under which g-frames (and the finite sum of g-frames) are stable under small perturbations.