Compact groups of operators on proportional quotients of l(1)(n)

It is proved that for arbitrary m is an element of N and for a sufficiently nontrivial compact group G of operators acting on a "typical" n-dimensiona l quotient X-n of l(1)(m) with m = (1 + delta)n, there is a constant c = c( delta) such that sup(parallel to x parallel to=1) integral(G)parallel to T(x)parallel to dh( G)(T) greater than or equal to c root n/log n.