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- W2943716497 abstract "We say that a mapping $f: X rightarrow Y$ between two real normed spaces is a phase-isometry if it satisfies the functional equation begin{eqnarray*} {|f(x)+f(y)|, |f(x)-f(y)|}={|x+y|, |x-y|} quad (x,yin X).end{eqnarray*} A generalized Mazur-Ulam question is whether every surjective phase-isometry is a multiplication of a linear isometry and a map with range ${-1, 1}$. This assertion is also an extension of a fundamental statement in the mathematical description of quantum mechanics, Wigner's theorem to real normed spaces. In this paper, we show that for every space $Y$ the problem is solved in positive way if $X$ is a smooth normed space, an $mathcal{L}^{infty}(Gamma)$-type space or an $ell^1(Gamma)$-space with $Gamma$ being an index set." @default.
- W2943716497 created "2019-05-09" @default.
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- W2943716497 date "2019-05-05" @default.
- W2943716497 modified "2023-10-15" @default.
- W2943716497 title "Phase-isometries on real normed spaces" @default.
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- W2943716497 doi "https://doi.org/10.48550/arxiv.1905.01637" @default.
- W2943716497 hasPublicationYear "2019" @default.
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