Unitary representations of finite abelian groups realizable by an action

Abstract

Let Γ be a finite abelian group and let H be an infinite-dimensional separable complex Hilbert space. We prove that the set of realizable by an action unitary representations of Γ on H is comeager in the space of all unitary representations of Γ on H.

Keywords

• Finite abelian group
• Unitary representation
• Group action
• Baire category