Naslov
On Wigner's theorem in smooth normed spaces

Autori
Ilišević, Dijana ; Turnšek, Aleksej

Izvornik
Aequationes mathematicae (0001-9054) 94 (2020); 1257-1267

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Wigner’s theorem ; isometry ; normed space

Sažetak
In this note we generalize the well-known Wigner's unitary-anti\-unitary theorem. For smooth normed spaces $X$ and $Y$ and a surjective mapping $f \colon X\to Y$ such that $| [f(x), f(y)]|=|[x, y]|$, $x, y\in X$, where $[\cdot, \cdot]$ is the unique semi-inner product, we show that $f$ is phase equivalent to either a linear or an anti-linear surjective isometry. When $X$ and $Y$ are smooth real normed spaces and $Y$ is strictly convex, we show that Wigner's theorem is equivalent to $\{; ; ; \|f(x)+f(y)\|, \|f(x)- f(y)\|\}; ; ; =\{; ; ; \|x+y\|, \|x-y\|\}; ; ; $, $x, y\in X$.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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