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Surjective L2-isometries on the Projection Lattice

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Abstract

Recently, Gehér and Šemrl have characterized the general form of surjective isometries of the set of all projections on an infinite-dimensional separable Hilbert space using unitaries and antiunitaries. In this paper, we study the surjective L2-isometries of the projection lattice of an infinite dimensional Hilbert space and show that every such isometry can also be described by unitaries and antiunitaries.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, P. R. China

    Li Guang Wang

  2. School of Mathematical Sciences, Chongqing Normal University, Chongqing, 401331, P. R. China

    Wen Ming Wu

  3. Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P. R. China

    Wei Yuan

  4. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, P. R. China

    Wei Yuan

Authors
  1. Li Guang Wang
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  2. Wen Ming Wu
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  3. Wei Yuan
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Corresponding author

Correspondence to Wen Ming Wu.

Additional information

Wang was supported in part by NFS of China (Grant Nos. 11871303, 11971463, 11671133) and NSF of Shandong Province (Grant No. ZR2019MA039); Wu was supported in part by NFS of China (Grant Nos. 11871127, 11971463) and Chongqing Science and Technology Commission (Grant No. cstc2019jcyj-msxmX0256); Yuan was supported in part by NFS of China (Grant Nos. 11871303, 11871127, 11971463)

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Wang, L.G., Wu, W.M. & Yuan, W. Surjective L2-isometries on the Projection Lattice. Acta. Math. Sin.-English Ser. 37, 825–834 (2021). https://doi.org/10.1007/s10114-021-0306-9

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  • DOI: https://doi.org/10.1007/s10114-021-0306-9

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