Abstract
In this paper we determine the structure of all so-called generalized isometries of the special unitary group which are transformations that respect any member of a large collection of generalized distance measures.
Similar content being viewed by others
References
Chan J.T., Li C.K., Sze N.S.: Isometries for unitarily invariant norms. Linear Algebra Appl. 399, 53–70 (2005)
J.T. Chan, C.K. Li, and C.C.N. Tu, A class of unitarily invariant norms on B(H), Proc. Amer. Math. Soc. 129 (2001), 1065–1076.
M.D. Choi, A.A. Jafarian, and H. Radjavi, Linear maps preserving commutativity, Linear Algebra Appl. 87 (1987), 227–241.
O. Hatori, Isometries on the special unitary group, in Function Spaces in Analysis, K. Jarosz, Edt. Contemporary Mathematics, Am. Math. Soc. 645, (2015), 119–134.
R.A. Horn and C. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1990.
L. Molnár, Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces, Lecture Notes in Mathematics, Vol. 1895, p. 236, Springer (2007).
L. Molnár, Jordan triple endomorphisms and isometries of unitary groups, Linear Algebra Appl. 439 (2013), 3518–3531.
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.), Operator Theory: Advances and Applications, 250 (2015), 311–342.
Author information
Authors and Affiliations
Corresponding author
Additional information
The main part of this research was done during the second author’s visit to the Department of Mathematics at Niigata University. He is very grateful for the warm hospitality he received from the first author and his colleagues. The second author was supported by the “Lendület” Program (LP2012-46/2012) of the Hungarian Academy of Sciences and by the Hungarian Scientific Research Fund (OTKA) Reg. No. K115383.
Rights and permissions
About this article
Cite this article
Hatori, O., Molnár, L. Generalized isometries of the special unitary group. Arch. Math. 106, 155–163 (2016). https://doi.org/10.1007/s00013-015-0856-0
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00013-015-0856-0