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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 14th 2019

added pointer to

• Valentine Bargman, Note on Wigner’s theorem on symmetry transformations, Journal of Mathematical Physics 5.7 (1964): 862-868 (doi:10.1063/1.1704188)
• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMay 14th 2019

and added this one (thanks to David R.):

• C. S. Sharma and D. F. Almeida, Additive isometries on a quaternionic Hilbert space, Journal of Mathematical Physics 31, 1035 (1990) (doi:10.1063/1.528779)
• CommentRowNumber3.
• CommentAuthorMiklós
• CommentTimeNov 14th 2020
• (edited Nov 14th 2020)

.

• CommentRowNumber4.
• CommentAuthorMiklós
• CommentTimeNov 28th 2021
There is a minor inaccuracy in the statment, since anti-unitary operators are not linear (they are anti-linear).
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