Abstract. The compactness of the integral of an operator-valued function is proven in an elementary way, generalizing an earlier result of Karl H. Hofmann, related to the Peter--Weyl theory of continuous representations of compact groups.

AMS Subject Classification (1991): 43A50, 43A77, 43A65

Received March 9, 2004, and in revised form September 9, 2004. (Registered under 5867/2009.)