Letαbe a flow on a Banach algebra B, and t 7→ut a continuous function from 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, where Adut...Letαbe a flow on a Banach algebra B, and t 7→ut a continuous function from 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, where Adut（B） , utBu-1t for any B ∈ B. β is said to be a cocycle perturbation of α. We show that if α, β are two flows on a nest algebra （or quasi-triangular algebra）, thenβ is a cocycle perturbation ofα. And the flows on a nest algebra （or quasi-triangular algebra） are all uniformly continuous.展开更多
文摘Letαbe a flow on a Banach algebra B, and t 7→ut a continuous function from 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, where Adut（B） , utBu-1t for any B ∈ B. β is said to be a cocycle perturbation of α. We show that if α, β are two flows on a nest algebra （or quasi-triangular algebra）, thenβ is a cocycle perturbation ofα. And the flows on a nest algebra （or quasi-triangular algebra） are all uniformly continuous.
