Abstract
Two notions of Bessel fusion multipliers have been recently appeared in the literature, but it seems that some questions of invertibility of fusion frame multipliers have not been satisfactorily answered. To achieve our main research goal, first we survey the approaches toward dual fusion frames existing in the literature and agree on the notion of duality for fusion frames in the sense of Kutyniok et al. (Oper Matrices 11:301–336, 2017). We then proposed a slightly modified version of those notions and analyze how our notion of Bessel fusion multipliers performs with respect to a list of desiderata which, to our minds, an invertible fusion frame multiplier should satisfy. Particularly, in contrast to the existing notions, we show that in many cases Bessel fusion multipliers in our sense behave similar to ordinary Bessel multipliers. Also, special attention is devoted to the study of invertible Bessel fusion multipliers.
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Sargazi, M., Javanshiri, H. & Fattahi, A. Fusion Frame Duals and Its Applications to Invertible Bessel Fusion Multipliers. Iran J Sci Technol Trans Sci 45, 945–954 (2021). https://doi.org/10.1007/s40995-021-01063-x
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DOI: https://doi.org/10.1007/s40995-021-01063-x