RETRACTED: THE WIGNER PROPERTY FOR CL-SPACES AND FINITE-DIMENSIONAL POLYHEDRAL BANACH SPACES (Retracted Article)

We say that a map f from a Banach space X to another Banach space Y is a phase-isometry if the equality {parallel to f(x) + f(y)parallel to, parallel to f(x) - f(y)parallel to} = {parallel to x + y parallel to, parallel to x - y parallel to} holds for all x, y is an element of 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 -> Y, there exists a phase function e : X -> {- 1, 1} such that epsilon . 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.