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THE WIGNER PROPERTY OF SMOOTH NORMED SPACES
Published online by Cambridge University Press: 09 May 2024
Abstract
We prove that every smooth complex normed space X has the Wigner property. That is, for any complex normed space Y and every surjective mapping $f: X\rightarrow Y$ satisfying
where $\mathbb {T}$ is the unit circle of the complex plane, there exists a function $\sigma : X\rightarrow \mathbb {T}$ such that $\sigma \cdot f$ is a linear or anti-linear isometry. This is a variant of Wigner’s theorem for complex normed spaces.
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- © The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
The first and second authors were supported by the Natural Science Foundation of Tianjin Municipal Science and Technology Commission (Grant No. 22JCYBJC00420) and the National Natural Science Foundation of China (Grant No. 12271402). The third author was supported by the National Natural Science Foundation of China (Grant Nos. 12201459 and 12071358).