We say that a map between two real normed spaces is a phase-isometry if holds for all . Two maps are called phase-equivalent if there is a phase function such that . By studying the properties of surjective phase-isometries on the Tsirelson space , we show that such maps are phase-equivalent to linear isometries. This gives a real version of Wigner’s theorem for the Tsirelson space.
"Wigner’s theorem on the Tsirelson space ." Ann. Funct. Anal. 10 (4) 515 - 524, November 2019. https://doi.org/10.1215/20088752-2019-0010