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WOVEN g-FRAMES IN HILBERT C<sup>∗</sup>-MODULES
Rajput, Ekta,Sahu, Nabin Kumar,Mishra, Vishnu Narayan The Kangwon-Kyungki Mathematical Society 2021 한국수학논문집 Vol.29 No.1
Woven frames are motivated from distributed signal processing with potential applications in wireless sensor networks. g-frames provide more choices on analyzing functions from the frame expansion coefficients. The objective of this paper is to introduce woven g-frames in Hilbert C∗-modules, and to develop its fundamental properties. In this investigation, we establish sufficient conditions under which two g-frames possess the weaving properties. We also investigate the sufficient conditions under which a family of g-frames possess weaving properties.
Controlled $K$-frames in Hilbert C*-modules
Ekta Rajput,Nabin Kumar Sahu,Vishnu Narayan Mishra 강원경기수학회 2022 한국수학논문집 Vol.30 No.1
Controlled frames have been the subject of interest because of their ability to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper, we introduce the notion of controlled $K$-frame or controlled operator frame in Hilbert $C^{*}$-modules. We establish the equivalent condition for controlled $K$-frame. We investigate some operator theoretic characterizations of controlled $K$-frames and controlled Bessel sequences. Moreover, we establish the relationship between the $K$-frames and controlled $K$-frames. We also investigate the invariance of a controlled $K$-frame under a suitable map $T$. At the end, we prove a perturbation result for controlled $K$-frame.