> Can you produce an example where there is even one interesting > operator-norm-continuous represenation? I guess "interesting" would > mean not essentially a direct sum of finite-dimensional > representations.
Yes, the left regular representation of a discrete infinite group. Similar action arises when G has two neighbourhoods of unity such that VU\subset U. Then G acts norm-continuously on the subspace of L_2(G) consisting of functions such that f(xU)=f(x) for all x.
I cannot think out less trivial examples, and this is why I'm asking the question.