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The wigner property for CL-spaces and finite-dimensional polyhedral Banach spaces
Published online by Cambridge University Press: 30 April 2021
Abstract
We say that a map $f$ from a Banach space $X$
to another Banach space $Y$
is a phase-isometry if the equality
. 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.
MSC classification
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- Research Article
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- Copyright
- Copyright © The Author(s) 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society
References
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