Controlled $g$-dual frames and their approximates in Hilbert spaces

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Hacettepe Journal of Mathematics and Statistics
Volume: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 RAMEZANİ

Pages : 421-429

Doi:10.15672/hujms.784819

View : 60 | Download : 11

Publication Date : 2022-04-01

Article Type : Research Paper

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

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