Unitary representations of the groups of measurable and continuous   functions with values in the circle
  We give a classification of unitary representations of certain Polish, not necessarily locally compact, groups: the groups of all measurable functions with values in the circle and the groups of all continuous functions on compact, second countable, zero-dimensional spaces with values in the circle. In the proofs of our classification results, certain structure theorems and factorization theorems for linear operators are used. 
Slawomir Solecki
math.RT math.FA