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Some Results on Fusion Frames and g-Frames

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Abstract

In this paper, we discuss some aspects where fusion frames and g-frames behave differently from frames. Several counterexamples to make clear their different behaviour are given. We also improve some results on g-frames. Moreover, we extend the notion of redundancy to g-frames and show that most of the desirable properties of lower and upper redundancies on frames and fusion frames can carry over g-frames. We also study the relationship between redundancy of g-frames and their dual g-frames, redundancy for infinite g-frames and the excess of g-frames.

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Authors and Affiliations

  1. Graduate University of Science and Technology, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

    Nguyen Quynh Nga

  2. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Hanoi, Vietnam

    Nguyen Quynh Nga

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  1. Nguyen Quynh Nga
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Correspondence to Nguyen Quynh Nga.

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Nga, N.Q. Some Results on Fusion Frames and g-Frames. Results Math 73, 75 (2018). https://doi.org/10.1007/s00025-018-0839-0

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  • DOI: https://doi.org/10.1007/s00025-018-0839-0

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