Transformations on the set of all n-dimensional subspaces of a Hilbert space preserving principal angles

摘要

Wigner's classical theorem on symmetry transformations plays a fundamentalrole in quantum mechanics. It can be formulated, for example, in the followingway: Every bijective transformation on the set L of all 1-dimensional subspacesof a Hilbert space H which preserves the angle between the elements of L isinduced by either a unitary or an antiunitary operator on H. The aim of thispaper is to extend Wigner's result from the 1-dimensional case to the case ofn-dimensional subspaces of H with n fixed.