Cocycle perturbation on Banach algebra

Let $\alpha$ be a flow on a Banach algebra $\mathfrak{B}$, and $t\longmapsto u_t$acontinuousfunctionon$$\mathbb{R}$$ into the group of invertible elements of $\mathfrak{B}$ such that $u_s\alpha_s(u_t )=u_{s+t}, s, t \in $\mathbb{R}$$\mathrm{.}Then$\beta_t=$Ad$u_t\circ\alpha_t, t\in $\mathbb{R}$$ is also a flow on $\mathfrak{B}$. $\beta$ is said to be a cocycle perturbation of $\alpha$. We show that if $\alpha ,\beta$ are two flows on nest algebra (or quasi-triangular algebra), then $\beta$ is a cocycle perturbation of $\alpha$. And the flows on nest algebra (or quasi-triangular algebra) are all uniformly continuous.