WIGNER’S THEOREM IN -TYPE SPACES
2017 ◽
Vol 97
(2)
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pp. 279-284
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Keyword(s):
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.
2015 ◽
Vol 38
(2)
◽
pp. 477-490
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1986 ◽
Vol 19
(2)
◽
pp. 205-210
◽
1988 ◽
Vol 30
(1)
◽
pp. 75-85
◽
2002 ◽
Vol 194
(2)
◽
pp. 248-262
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Keyword(s):
2017 ◽
Vol 96
(3)
◽
pp. 479-486
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Keyword(s):
2018 ◽
Vol 97
(3)
◽
pp. 459-470
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1969 ◽
Vol 12
(6)
◽
pp. 837-846
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