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Published Online: 04 June 1998
Accepted: December 1989

Additive isometries on a quaternionic Hilbert space

Journal of Mathematical Physics 31, 1035 (1990); https://doi.org/10.1063/1.528779
C. S. Sharma and D. F. Almeida
more...View Affiliations
  • Mathematical Research Unit, University of London, Birkbeck College, 43 Gordon Square, London, WC1H 0PD, England
Abstract
A systematic study of additive isometries on a quaternionic Hilbert space is presented. A number of new results describing the properties of such operators are proved. The work culminates in the first mathematical proof of Wigner’s theorem for quaternionic Hilbert spaces of dimension other than 2 which asserts that any operator which preserves the absolute value of the inner product on a quaternionic Hilbert space is equivalent, in the sense of differing pointwise by a mere phase factor, to a linear isometry. A complete and concise description of the exceptional situation in a two‐dimensional quaternionic Hilbert space is given.

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