- Hacettepe Journal of Mathematics and Statistics
- Vol: 51 Issue: 2
- Controlled $g$-dual frames and their approximates in Hilbert spaces
Controlled $g$-dual frames and their approximates in Hilbert spaces
Authors : Sayyed Mehrab Ramezani
Pages : 421-429
Doi:10.15672/hujms.784819
View : 13 | Download : 5
Publication Date : 2022-04-01
Article Type : Research
Abstract :In this paper, we introduced and characterized the controlled $g$-duals of a frame in a separable Hilbert space $\mathcal{H}$ . Afterwards, we obtained new $C$-controlled $g$-dual frames from the given $C$-controlled $g$-dual frames. In addition, the approximation for controlled $g$-dual frames was defined and some of their properties were investigated. Finally, we characterized the relationship between approximately $C$-controlled dual and $C$-controlled $g$-dual.Keywords : frames, controlled frames, g-dual frame, approximate g-dual