# Start a new discussion

## Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

## Site Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 14th 2019

• 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).
• CommentRowNumber5.
• CommentAuthorMiklós
• CommentTimeJul 13th 2022
• (edited Jul 13th 2022)

Is this theorem true at all? Let the function $f$ map $(z_1,z_2,\dots)$ to $(\overline z_1, z_2,\dots)$ where the coordinates refer to a Hilbert basis. This is a surjective norm-preserving transformation but isn’t unitary or anti-unitary even up to phase.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeJul 13th 2022

The statement in the entry was missing the condition that the map sends lines to lines, i.e. that it is a map of projective spaces. I have made a quick edit, but no time for more for the moment.

• CommentRowNumber7.
• CommentAuthorUrs
• CommentTimeJul 13th 2022

I have now expanded a fair bit, written out the actual statement (starting in a new section “Preliminaries” here) and also adding an “Idea”-section (here).