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A non-injective version of Wigner's theorem (1808.02783v4)

Published 8 Aug 2018 in math-ph, math.FA, and math.MP

Abstract: Let $H$ be a complex Hilbert space and let ${\mathcal F}{s}(H)$ be the real vector space of all self-adjoint finite rank operators on $H$. We prove the following non-injective version of Wigner's theorem: every linear operator on ${\mathcal F}{s}(H)$ sending rank one projections to rank one projections (without any additional assumption) is either induced by a linear or conjugate-linear isometry or constant on the set of rank one projections.

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