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On perturbations of woven pairs of frames

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Abstract

In this note, we prove some results related to small perturbations of a frame for a Hilbert space \({{\mathcal {H}}}\) in order to have a woven pair for \({{\mathcal {H}}}\). Our results complete those known in the literature. In addition we study a necessary condition for a woven pair, that resembles a characterization for Riesz frames.

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References

  1. Antezana, J., G. Corach, D. Stojanoff, and M. Ruiz. 2005. Weighted projections and Riesz frames. Linear Algebra and its Applications 402: 367–389.

    Article  MathSciNet  Google Scholar 

  2. Bemrose, T., P.G. Casazza, K. Gröchenig, M.C. Lammers, and R.G. Lynch. 2016. Weaving frames. Operational Matrices 10 (4): 1093–1116.

    Article  MathSciNet  Google Scholar 

  3. Casazza P.G., and R. G. Lynch. 2015. Weaving properties of Hilbert space frames, Proc. SampTA , 110–114.

  4. Casazza, P.G., D. Freeman, and R.G. Lynch. 2016. Weaving Schauder frames. Journal of Approximation Theory 211: 42–60.

    Article  MathSciNet  Google Scholar 

  5. Christensen, O. 1996. Frames containing a Riesz basis and approximation of the frame coefficients using finite dimensional methods. Journal of Mathematical Analysis and Applications 199: 256–270.

    Article  MathSciNet  Google Scholar 

  6. Deepshikha, S.G., and L.K. Vashisht. 2017. On Continuous weaving frames. Advances in Pure and Applied Mathematics 8 (1): 15–31.

    MathSciNet  MATH  Google Scholar 

  7. Deepshikha, S.G., and L.K. Vashisht. 2018. Weaving K- Frames in Hilbert Spaces. Results in Mathematics 73: 73–81.

    Article  MathSciNet  Google Scholar 

  8. Deepshikha, S.G., Vashisht, L.K., and G. Verma. 2017. On weaving fusion frames for Hilbert spaces, 2017 International Conference on Sampling Theory and Applications (SampTA), Tallin, 381–385, https://doi.org/10.1109/SAMPTA.2017.8024363.

  9. Deutsch, F. 1995. The angle between subspaces in Hilbert space. In Approximation theory, wavelets and applications, 107–130. Netherlands: Springer.

    Chapter  Google Scholar 

  10. Ding, J., and L.J. Huang. 1996. Perturbation of generalized inverses of linear operators in Hilbert spaces. Journal of Mathematical Analysis and Applications 198: 505–516.

    Article  MathSciNet  Google Scholar 

  11. Li, D., J. Leng, T. Huang, and X. Li. 2020. On Weaving g-Frames for Hilbert Spaces. Complex Analysis and Operator Theory. https://doi.org/10.1007/s11785-020-00991-7.

    Article  MathSciNet  MATH  Google Scholar 

  12. Neyshaburi, F.A., and A. A. Arefijamaal, Weaving Hilbert space fusion frames, preprint, arXiv:1802.03352.

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Acknowledgements

This research is partially supported by by CONICET (PIP 1505/15) and Universidad Nacional de La Plata (UNLP 11 X829).

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Authors and Affiliations

  1. CMaLP, FCE-UNLP, La Plata, Argentina

    Pablo Calderón & Mariano A. Ruiz

  2. IAM, CONICET, Buenos Aires, Argentina

    Pablo Calderón & Mariano A. Ruiz

Authors
  1. Pablo Calderón
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  2. Mariano A. Ruiz
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Correspondence to Mariano A. Ruiz.

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Communicated by Samy Ponnusamy.

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Calderón, P., Ruiz, M.A. On perturbations of woven pairs of frames. J Anal 30, 1011–1021 (2022). https://doi.org/10.1007/s41478-022-00389-y

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  • DOI: https://doi.org/10.1007/s41478-022-00389-y

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