WIGNER’S THEOREM IN ${\mathcal{L}}^{\infty }(\unicode[STIX]{x1D6E4})$ -TYPE SPACES

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 $...

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Bibliographic Details

Published in:	Bulletin of the Australian Mathematical Society Vol. 97; no. 2; pp. 279 - 284
Main Authors:	JIA, WEIKE, TAN, DONGNI
Format:	Journal Article
Language:	English
Published:	Cambridge, UK Cambridge University Press 01.04.2018
Subjects:	Mathematical functions L ∞ -type spaces Wigner’s theorem primary 46B03 phase equivalent secondary 46B04
ISSN:	0004-9727, 1755-1633
Online Access:	Get full text
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