  We establish an operator-theoretic uncertainty principle over arbitrary
compact groups, generalizing several previous results. As a consequence, we
show that if f is in L^2(G), then the product of the measures of the supports
of f and its Fourier transform ^f is at least 1; here, the dual measure is
given by the sum, over all irreducible representations V, of d_V rank(^f(V)).
For finite groups, our principle implies the following: if P and R are
projection operators on the group algebra C[G] such that P commutes with
projection onto each group element, and R commutes with left multiplication,
then the squared operator norm of PR is at most rank(P)rank(R)/|G|.
