Naslov
A variant of Wigner's theorem in normed spaces

Autori
Ilišević, Dijana ; Turnšek, Aleksej

Izvornik
Mediterranean journal of mathematics (1660-5446) 18 (2021); 148, 11

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

Ključne riječi
Wigner's theorem ; isometry ; normed space ; support functional ; projective geometry

Sažetak
Let $X$ and $Y$ be normed spaces over $\mathbb{; ; ; F}; ; ; \in \{; ; ; \mathbb{; ; ; R}; ; ; , \mathbb{; ; ; C}; ; ; \}; ; ; $ and $f \colon X \to Y$ a surjective mapping. Suppose that $|\phi_{; ; ; f(y)}; ; ; (f(x))|=|\phi_y(x)|$ holds for all $x, y\in X$ and all support functionals $\phi_{; ; ; f(y)}; ; ; $ at $f(y)$ and $\phi_y$ at $y$, or equivalently, suppose that for all semi-inner products on $X$ and $Y$, compatible with given norms, $\vert [f(x), f(y)] \vert = \vert [x, y] \vert$ holds for all $x, y \in X$. Then $f=\sigma U$, where $\sigma \colon X \to \mathbb{; ; ; F}; ; ; $ is a phase function, and $U \colon X \to Y$ is a linear or a conjugate linear isometry.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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