WebWe present an analogue of Uhlhorn’s version of Wigner’s theorem on symmetry transformations for the case of indefinite inner product spaces. This significantly generalizes a result of Van den Broek. Web28 Jan 2024 · The strength and importance of Uhlhorn’s theorem is that it requires that the map keeps the orthogonality of rank-one projections, or equivalently of non-normalized vectors (or rays). A transformation mapping an orthonormal basis onto an orthonormal basis is clearly a unitary or anti-unitary transform; however, this result is far from obvious ...
Entropy Free Full-Text Revisiting Born’s Rule through Uhlhorn …
Web6 Sep 2002 · Abstract We present an analogue of Uhlhorn's version of Wigner's theorem on symmetry transformations for the case of indefinite inner product spaces. This significantly generalizes a result of Van den Broek. The proof is based on our main theorem, which describes the form of all bijective transformations on the set of all rank-one idempotents … Web1 Oct 2002 · We present an analogue of Uhlhorn's version of Wigner's theorem on symmetry transformations for the case of indefinite inner product spaces. This significantly generalizes a result of Van den Broek. idiots guide to backgammon
[PDF] Linear orthogonality preservers of Hilbert C ∗ -modules over ...
WebThe Wigner theorem, in its Uhlhorn’s formulation, states that a bijective transformation of the set of all one-dimensional linear subspaces of a complex Hilbert space which … Web21 May 1997 · However, there is a counterexample for Uhlhorn’s version of Wigner’s theorem for such state space. In this note we prove that in order that the description of … Web12 Jul 2012 · space H determine each other, through a polarization formula. By the Uhlhorn theorem (which generalized the famous Wigner theorem; see, e.g., [18]), the or thogonality … isscc highlight