Surjective L2-isometries on the Projection Lattice

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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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. (2021). https://doi.org/10.1007/s10114-021-0306-9

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Keywords

  • Wigner’s theorem
  • L 2-isometries
  • projections
  • tracial weight

MR(2010) Subject Classification

  • 47B49
  • 54E40