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Erasures and Equalities for Fusion Frames in Hilbert Spaces

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Abstract

Fusion frames are widely studied recently due to its many kinds of applications. In this paper we focus on the erasure of a fusion frame; we use a bounded linear operator to equivalently characterize a given fusion frame to be robust to an erasure of any numbers of elements; it turns out that our result is more general and covers some important results previously obtained by Asgari, Casazza, and Kutyniok. We also present a more general equality result for any fusion frame (not restricted to be tight), which improves the fusion version of a theorem obtained by Li and Sun.

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Acknowledgments

The authors thank the anonymous referee for valuable comments, which greatly improve the presentation of the manuscript. This work is partly supported by the Natural Science Foundation of Fujian Province, China (Grant No. 2012J01005, 2014J01007), the Science and Technology Funds from the Fuzhou University, China (Grant No. 2012-XQ-29, 2012-XY-21), and the Scientific Research Start-up Foundation of Fuzhou University, China (Grant No. 022410).

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Authors and Affiliations

  1. Department of Mathematics and Computer science, Fuzhou University, Fuzhou, 350116, People’s Republic of China

    Xiang-chun Xiao & Yu-can Zhu

  2. College of Computer and Information, Fujian Agriculture and Forestry University, Fuzhou, 350002, People’s Republic of China

    Ming-ling Ding

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  1. Xiang-chun Xiao
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  2. Yu-can Zhu
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  3. Ming-ling Ding
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Correspondence to Xiang-chun Xiao.

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Lee See Keong.

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Xiao, Xc., Zhu, Yc. & Ding, Ml. Erasures and Equalities for Fusion Frames in Hilbert Spaces. Bull. Malays. Math. Sci. Soc. 38, 1035–1045 (2015). https://doi.org/10.1007/s40840-014-0071-3

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  • DOI: https://doi.org/10.1007/s40840-014-0071-3

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