Unitary Representations of Inductive Limits of Commutative Locally Compact Groups

Abstract

This section could also be called: families of commuting unitary operators. But here we will be mainly concerned with commutative groups of unitary operators, the study of which is reduced to the study of countable collections of commuting self-adjoint operators. Regardless the fact that these groups of unitary operators are not representations of locally compact groups, they have a number of properties that make them like representations of finite-dimensional commutative Lie groups.