If Tt = eZt is a positive one-parameter contraction semigroup acting on lp(X) where X is a countable set and 1 ≤ p < ∞, then the peripheral point spectrum P of Z cannot contain any non-zero elements. The same holds for Feller semigroups acting on Lp(X) if X is locally compact.

We show the sum of the first k Lyapunov exponents of linear cocycles is an upper semicontinuous function in the L topologies, for any 1 ≤ p ≤ ∞ and k. This fact, together with a result from Arnold and Cong, implies that the Lyapunov exponents of the L-generic cocycle, p < ∞, are all equal.