Wigner’s theorem in Hilbert $C^*$-modules over $C^*$-algebras of compact operators
Wigner’s theorem in Hilbert $C^*$-modules over $C^*$-algebras of compact operators
Let $W$ be a Hilbert $C^*$-module over the $C^*$-algebra $\mathcal {A}\not = \boldsymbol {C}$ 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 ${\mathcal A}$-valued inner product is of the form $Tv=\varphi (v)Uv, v …