Cocycle perturbation on Banach algebra

Details Cocycle perturbation on Banach algebra Cocycle perturbation on Banach algebra

2010-08-31

arxiv.org/abs/1008.5249v1

Mathematics

Operator Algebras

9 pages

Scientific paper

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.

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