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We give a classification of unitary representations of certain Polish, notnecessarily locally compact, groups: the groups of all measurable functionswith values in the circle and the groups of all continuous functions oncompact, second countable, zero-dimensional spaces with values in the circle.In the proofs of our classification results, certain structure theorems andfactorization theorems for linear operators are used.

Unitary representations of the groups of measurable and continuous functions with values in the circle