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On certain generalized isometries of the special orthogonal group

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In this paper we explore the structure of certain generalized isometries of the special orthogonal group SO(n) which are transformations that leave any member of a large class of generalized distance measures invariant.

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References

  1. T. Abe, S. Akiyama, and O. Hatori, Isometries of the special orthogonal group, Linear Algebra Appl. 439 (2013), 174–188.

    Article  MathSciNet  MATH  Google Scholar 

  2. M. Brin and G. Stuck, Introduction to Dynamical Systems, Cambridge University Press, Cambridge, 2002.

    Book  MATH  Google Scholar 

  3. M. Gaál and R. M. Guralnick, On isometry groups of self-adjoint traceless and skew-symmetric matrices, submitted, available at arXiv:1709.04507.

  4. R. M. Guralnick and C. K. Li, Invertible preservers and algebraic groups III: preservers of unitary similarity (congruence) invariants and overgroups of some unitary subgroups, Linear Multilinear Algebra 43 (1997), 257–282.

    Article  MathSciNet  MATH  Google Scholar 

  5. O. Hatori, Isometries of the unitary groups in \(C^{*}\)-algebras, Studia Math. 221 (2014), 61–86.

    Article  MathSciNet  MATH  Google Scholar 

  6. O. Hatori and L. Molnár, Generalized isometries of the special unitary group, Arch. Math. 106 (2016), 155–163.

    Article  MathSciNet  MATH  Google Scholar 

  7. O. Hatori and L. Molnár, Isometries of the unitary group, Proc. Amer. Math. Soc. 140 (2012), 2141–2154.

    Article  MathSciNet  MATH  Google Scholar 

  8. O. Hatori and L. Molnár, Spectral conditions for Jordan \(*\)-isomorphisms on operator algebras, Studia Math. 236 (2017), 101–126.

    Article  MathSciNet  MATH  Google Scholar 

  9. Du Q. Huynh, Metrics for 3D rotations: comparison and analysis, J. Math. Imaging Vis. 35 (2009), 155–164.

    Article  Google Scholar 

  10. C. K. Li, Some aspects of the theory of norms, Linear Algebra Appl. 94 (1994), 71–100.

    Article  MathSciNet  MATH  Google Scholar 

  11. C. K. Li and N. K. Tsing, Duality between some linear preserver problems. III. c-Spectral norms and (skew)-symmetric matrices with fixed singular values, Linear Algebra Appl. 143 (1991), 67–97.

    Article  MathSciNet  MATH  Google Scholar 

  12. M. Moakher, Means and averaging in the group of rotations, SIAM J. Matrix Anal. Appl. 24 (2002), 1–16.

    Article  MathSciNet  MATH  Google Scholar 

  13. L. Molnár, General Mazur-Ulam type theorems and some applications, In: Operator Semigroups Meet Complex Analysis, Harmonic Analysis and Mathematical Physics, W. Arendt, R. Chill, Y. Tomilov (Eds.), 311–342, Oper. Theory Adv. Appl., 250, Birkhäuser/Springer, Cham, 2015.

  14. S. Sakai, On the group isomorphism of unitary groups in \(AW^{*}\) algebras, Tohoku Math. J. 7 (1955), 87–95.

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Marcell Gaál.

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Gaál, M. On certain generalized isometries of the special orthogonal group. Arch. Math. 110, 61–70 (2018). https://doi.org/10.1007/s00013-017-1122-4

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  • DOI: https://doi.org/10.1007/s00013-017-1122-4

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