  Let $\alpha$ be a flow on a Banach algebra $\mathfrak{B}$, and $t\longmapsto
u_t$ a continuous function on $\mathbb{R}$ into the group of invertible
elements of $\mathfrak{B}$ such that $u_s\alpha_s(u_t )=u_{s+t}, s, t \in
\mathbb{R}$. 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.
