Control Fusion Frames in Hilbert Spaces and Their Dual

Authors

  • Habib Shakoory Department of Mathematics, Shabestar Branch, Islamic Azad University , Shabestar, Iran
  • Reza Ahmadi Research Institute for Fundamental Science, University of Tabriz, Tabriz, Iran.
  • Naghi Behzadi Research Institute for Fundamental Science, University of Tabriz, Tabriz, Iran.
  • Susan Nami Faculty of Physic, University of Tabriz, Iran.

Keywords:

frame, hilbert space, controlled frame

Abstract

Controlled frames in Hilbert spaces have been introducedby Balazs, Antoine and Grybos to improve the numerical output of inrelation to algorithms for inverting the frame operator. In this paper,we introduce some new concepts and show results on controlled fusionframes for Hilbert spaces. It is shown that controlled fusion framesare a generalization of fusion frames giving a generalized way to obtainnumerical advantage in the sense of preconditioning to check the fusionframe condition. For this end, we introduce the notion of Q-duality forControlled fusion frames. Also, we survey the robustness of controlledfusion frames under some perturbations.

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Published

2021-11-10

Issue

Vol. 16

Section

Vol. 16, No. 9, (2022)

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