Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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CONTROLLED K-FRAMES IN HILBERT C*-MODULES

  • Rajput, Ekta (Dhirubhai Ambani Institute of Information and Communication Technology) ;
  • Sahu, Nabin Kumar (Dhirubhai Ambani Institute of Information and Communication Technology) ;
  • Mishra, Vishnu Narayan (Department of Mathematics, Indira Gandhi National Tribal University)
  • Received : 2021.10.04
  • Accepted : 2022.02.08
  • Published : 2022.03.30
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Abstract

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.

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Acknowledgement

The authors are thankful to the anonymous referees for their valuable suggestions and comments that significantly improved the presentation and correctness of this paper.

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