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Computing the Distance Between Frames and Between Subspaces of a Hilbert Space

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Frames and Other Bases in Abstract and Function Spaces

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

A fundamental notion in Hilbert space frame theory is to compute the distance between frames and the distance between subspaces of a Hilbert space. One space these problems arise is with a number of algorithms which serve to approximate frame operators or inverse operators [5]. There are six standard distance functions used in frame theory. In this paper we will establish the exact relationship between all of these distance functions.

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References

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  5. O. Christensen, An Introduction to Frames and Riesz Bases (Birkhäuser, Boston, 2003)

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Acknowledgements

The authors were supported by NSF DMS 1609760; NSF ATD 1321779; and ARO W911NF-16-1-0008.

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Authors and Affiliations

  1. Mathematics Department, University of Missouri, Columbia, MO, 65211, USA

    Travis Bemrose, Peter G. Casazza, Desai Cheng & John Haas

  2. Mathematics Department, University of Alabama, Tuscaloosa, AL, 35487, USA

    Hanh Van Nguyen

Authors
  1. Travis Bemrose
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  2. Peter G. Casazza
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  3. Desai Cheng
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  4. John Haas
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  5. Hanh Van Nguyen
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Corresponding author

Correspondence to Travis Bemrose .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Temple University, Philadelphia, Pennsylvania, USA

    Isaac Pesenson

  2. School of Mathematics and Statistics, The University of New South Wales, Sydney, New South Wales, Australia

    Quoc Thong Le Gia

  3. Department of Mathematics, The Graduate Center, CUNY, New York, New York, USA

    Azita Mayeli

  4. Institute of Mathematical Sciences, Claremont Graduate University, Claremont, California, USA

    Hrushikesh Mhaskar

  5. Department of Mathematics, City University of Hong Kong, Kowloon Tong, Hong Kong

    Ding-Xuan Zhou

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Bemrose, T., Casazza, P.G., Cheng, D., Haas, J., Van Nguyen, H. (2017). Computing the Distance Between Frames and Between Subspaces of a Hilbert Space. In: Pesenson, I., Le Gia, Q., Mayeli, A., Mhaskar, H., Zhou, DX. (eds) Frames and Other Bases in Abstract and Function Spaces. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-55550-8_5

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