Duality relations associated with weak g-R-duals. Issue 20 (19th December 2022)

• Record Type: Journal Article
• Authors: Li, Yun-Zhang; Dong, Jian
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 20(2022)
• Page Start: 5482
• Page End: 5501
• Publication Date: 2022-12-19
• Subjects: Frame -- g-frame -- g-R-dual -- weak g-R-dual -- duality principle; 42C15; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2021.1918052
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : Recently, duality principles in g -frame theory were studied. This paper addresses a relaxation of g -R-duals. We introduce the notion of weak g -R-dual in g -frame theory setting, and present the link between frame properties of a bounded operator sequence and its weak g -R-duals. Using weak g -R-duals, we characterize g -frames and (unitary) equivalence between g -frames. And using pseudo-inverse operators, we represent the canonical duals of weak g -R-duals. Some examples are also provided.