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- W4242796787 abstract "Abstract We say that a map $f$ from a Banach space $X$ to another Banach space $Y$ is a phase-isometry if the equality [ {|f(x)+f(y)|, |f(x)-f(y)|}={|x+y|, |x-y|} ] holds for all $x,,yin X$ . A Banach space $X$ is said to have the Wigner property if for any Banach space $Y$ and every surjective phase-isometry $f : Xrightarrow Y$ , there exists a phase function $varepsilon : X rightarrow {-1,,1}$ such that $varepsilon cdot f$ is a linear isometry. We present some basic properties of phase-isometries between two real Banach spaces. These enable us to show that all finite-dimensional polyhedral Banach spaces and CL-spaces possess the Wigner property." @default.
- W4242796787 created "2022-05-12" @default.
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- W4242796787 date "2021-06-04" @default.
- W4242796787 modified "2023-10-18" @default.
- W4242796787 title "RETRACTED – The wigner property for CL-spaces and finite-dimensional polyhedral banach spaces" @default.
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- W4242796787 doi "https://doi.org/10.1017/s0013091521000250" @default.
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