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- Wigner-type theorems for Hilbert Grassmannians by Mark Pankov
- Bull. Amer. Math. Soc. 59 (2022), 289-292
- Additional book information: London Mathematical Society Lecture Note Series, Vol. 460, Cambridge University Press, Cambridge, 2020, viii+145 pp., ISBN 9781108800327
- V. Bargmann, Note on Wigner’s theorem on symmetry operations, J. Mathematical Phys. 5 (1964), 862–868. MR 164620, DOI 10.1063/1.1704188
- Rajendra Bhatia, Matrix analysis, Graduate Texts in Mathematics, vol. 169, Springer-Verlag, New York, 1997. MR 1477662, DOI 10.1007/978-1-4612-0653-8
- Fernanda Botelho, James Jamison, and Lajos Molnár, Surjective isometries on Grassmann spaces, J. Funct. Anal. 265 (2013), no. 10, 2226–2238. MR 3091813, DOI 10.1016/j.jfa.2013.07.017
- Wei-Liang Chow, On the geometry of algebraic homogeneous spaces, Ann. of Math. (2) 50 (1949), 32–67. MR 28057, DOI 10.2307/1969351
- György Pál Gehér and Peter emrl, Isometries of Grassmann spaces, J. Funct. Anal. 270 (2016), no. 4, 1585–1601. MR 3447720, DOI 10.1016/j.jfa.2015.11.018
- György Pál Gehér and Peter emrl, Isometries of Grassmann spaces, II, Adv. Math. 332 (2018), 287–310. MR 3810254, DOI 10.1016/j.aim.2018.05.012
- György Pál Gehér, Symmetries of projective spaces and spheres, Int. Math. Res. Not. IMRN 7 (2020), 2205–2240. MR 4089448, DOI 10.1093/imrn/rny100
- György Pál Gehér, Wigner’s theorem on Grassmann spaces, J. Funct. Anal. 273 (2017), no. 9, 2994–3001. MR 3692328, DOI 10.1016/j.jfa.2017.06.011
- G.P. Gehér, and M. Mori, The structure of maps on the space of all quantum pure states that preserve a fixed quantum angle, Int. Math. Res. Not. IMRN (to appear).
- W. Gu, M. Ma, J. Shen, and W. Shi, Lp-isometries of Grassmann spaces in factors of type II.
- Máté Győry, Transformations on the set of all $n$-dimensional subspaces of a Hilbert space preserving orthogonality, Publ. Math. Debrecen 65 (2004), no. 1-2, 233–242. MR 2075266
- Camille Jordan, Essai sur la géométrie à $n$ dimensions, Bull. Soc. Math. France 3 (1875), 103–174 (French). MR 1503705
- Chi-Kwong Li, Lucijan Plevnik, and Peter emrl, Preservers of matrix pairs with a fixed inner product value, Oper. Matrices 6 (2012), no. 3, 433–464. MR 2987018, DOI 10.7153/oam-06-29
- Michiya Mori, Isometries between projection lattices of von Neumann algebras, J. Funct. Anal. 276 (2019), no. 11, 3511–3528. MR 3944303, DOI 10.1016/j.jfa.2018.10.011
- Lajos Molnár, Transformations on the set of all $n$-dimensional subspaces of a Hilbert space preserving principal angles, Comm. Math. Phys. 217 (2001), no. 2, 409–421. MR 1821230, DOI 10.1007/PL00005551
- Wenhua Qian, Liguang Wang, Wenming Wu, and Wei Yuan, Wigner-type theorem on transition probability preserving maps in semifinite factors, J. Funct. Anal. 276 (2019), no. 6, 1773–1787. MR 3912790, DOI 10.1016/j.jfa.2018.05.019
- Peter emrl, Orthogonality preserving transformations on the set of $n$-dimensional subspaces of a Hilbert space, Illinois J. Math. 48 (2004), no. 2, 567–573. MR 2085427
- U. Uhlhorn, Representation of symmetry transformations in quantum mechanics, Ark. Fysik 23 (1963), 307–340.
- Eugen Wigner, Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren, J. W. Edwards, Ann Arbor, Michigan, 1944 (German). MR 0010584
- Reviewer: György Pál Gehér
- Affiliation: Department of Mathematics and Statistics, University of Reading, Whiteknights, P.O. Box 220, Reading RG6 6AX, United Kingdom
- Email: gehergyuri@gmail.com, G.P.Geher@reading.ac.uk
- Journal: Bull. Amer. Math. Soc. 59 (2022), 289-292
- DOI: https://doi.org/10.1090/bull/1743
- Published electronically: June 21, 2021
- Review Copyright: © Copyright 2021 American Mathematical Society