engleski

Wigner's theorem in Hilbert C*-modules over C*-algebras of compact operators

Let $W$ be a Hilbert \cez-module over the \cez-algebra \as of all compact operators on a Hilbert space. It is proved that any function $T: W \rightarrow W$ which preserves the absolute value of the \ass-valued inner product is of the form $Tv=\varphi(v)Uv, \, v \in W$, where $\varphi$ is a phase function and $U$ is an \ass-linear isometry. The result generalizes Moln\' ar's extension of Wigner's classical unitary-antiunitary theorem.

C*-algebra Hilbert C*-module compact operator Wigner's theorem

nije evidentirano