WIGNER’S THEOREM IN -TYPE SPACES

Author:

JIA WEIKE,TAN DONGNIORCID

Abstract

We investigate surjective solutions of the functional equation $$\begin{eqnarray}\displaystyle \{\Vert f(x)+f(y)\Vert ,\Vert f(x)-f(y)\Vert \}=\{\Vert x+y\Vert ,\Vert x-y\Vert \}\quad (x,y\in X), & & \displaystyle \nonumber\end{eqnarray}$$ where $f:X\rightarrow Y$ is a map between two real ${\mathcal{L}}^{\infty }(\unicode[STIX]{x1D6E4})$-type spaces. We show that all such solutions are phase equivalent to real linear isometries. This can be considered as an extension of Wigner’s theorem on symmetry for real ${\mathcal{L}}^{\infty }(\unicode[STIX]{x1D6E4})$-type spaces.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Cited by 13 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Min-phase-isometries on the unit sphere of $$\mathcal {L}^\infty (\Gamma )$$-type spaces;Aequationes mathematicae;2024-09-10

2. Phase-isometries between the positive cones of the Banach space of continuous real-valued functions;Annals of Functional Analysis;2024-08-08

3. On a universal inequality for approximate phase isometries;Acta Mathematica Scientia;2024-02-14

4. On approximate phase isometries;Annals of Functional Analysis;2021-12-20

5. A Variant of Wigner’s Theorem in Normed Spaces;Mediterranean Journal of Mathematics;2021-06-06

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