Cocycle perturbation on Banach algebra

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Let α be a flow on a Banach algebra B, and t uₜ a continuous function on R into the group of invertible elements of B such that uₛαₛ(uₜ)=uₛ₊ₜ, s, t ∈ R. Then βₜ=Aduₜ∘αₜ, t∈ R is also a flow on B. β is said to be a cocycle perturbation of α. We show that if α,β are two flows on nest algebra (or quasi-triangular algebra), then β is a cocycle perturbation of α. And the flows on nest algebra (or quasi-triangular algebra) are all uniformly continuous.