2 results
RETRACTED – The wigner property for CL-spaces and finite-dimensional polyhedral banach spaces
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 64 / Issue 3 / August 2021
- Published online by Cambridge University Press:
- 04 June 2021, pp. 717-733
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- Article
- Export citation
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We say that a map $f$
from a Banach space $X$
to another Banach space $Y$
is a phase-isometry if the equality
\[ \{\|f(x)+f(y)\|, \|f(x)-f(y)\|\}=\{\|x+y\|, \|x-y\|\} \]holds for all $x,\,y\in X$
. A Banach space $X$
is said to have the Wigner property if for any Banach space $Y$
and every surjective phase-isometry $f : X\rightarrow Y$
, there exists a phase function $\varepsilon : X \rightarrow \{-1,\,1\}$
such that $\varepsilon \cdot f$
is a linear isometry. We present some basic properties of phase-isometries between two real Banach spaces. These enable us to show that all finite-dimensional polyhedral Banach spaces and CL-spaces possess the Wigner property.
The wigner property for CL-spaces and finite-dimensional polyhedral Banach spaces
- Part of
-
- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 64 / Issue 2 / May 2021
- Published online by Cambridge University Press:
- 30 April 2021, pp. 183-199
-
- Article
- Export citation
-
We say that a map $f$
from a Banach space $X$
to another Banach space $Y$
is a phase-isometry if the equality
\[ \{\|f(x)+f(y)\|, \|f(x)-f(y)\|\}=\{\|x+y\|, \|x-y\|\} \]holds for all $x,\,y\in X$
. A Banach space $X$
is said to have the Wigner property if for any Banach space $Y$
and every surjective phase-isometry $f : X\rightarrow Y$
, there exists a phase function $\varepsilon : X \rightarrow \{-1,\,1\}$
such that $\varepsilon \cdot f$
is a linear isometry. We present some basic properties of phase-isometries between two real Banach spaces. These enable us to show that all finite-dimensional polyhedral Banach spaces and CL-spaces possess the Wigner property.
