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Perturbations of frames

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Abstract

In this paper, we give some sufficient conditions under which perturbations preserve Hilbert frames and near-Riesz bases. Similar results are also extended to frame sequences, Riesz sequences and Schauder frames. It is worth mentioning that some of our perturbation conditions are quite different from those used in the previous literatures on this topic.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, P. R. China

    Dong Yang Chen

  2. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, P. R. China

    Lei Li

  3. Department of Mathematics, University of Memphis, Memphis, TN, 38152-3240, USA

    Ben Tuo Zheng

Authors
  1. Dong Yang Chen
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  2. Lei Li
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  3. Ben Tuo Zheng
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Corresponding author

Correspondence to Lei Li.

Additional information

The first author is supported by National Natural Science Foundation of China (Grant Nos. 10701063 and 11001231) and the Fundamental Research Funds for the Central Universities (Grant No. 2011121039), who is a participant in the NSF Workshop in Analysis and Probability, Texas AM University; the second author is supported by National Natural Science Foundation of China (Grant Nos. 11301285 and 11371201); the third author is supported by NSF (Grant No. DMS-1200370)

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Chen, D.Y., Li, L. & Zheng, B.T. Perturbations of frames. Acta. Math. Sin.-English Ser. 30, 1089–1108 (2014). https://doi.org/10.1007/s10114-014-2804-5

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  • DOI: https://doi.org/10.1007/s10114-014-2804-5

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