Year: 2014
Communications in Mathematical Research , Vol. 30 (2014), Iss. 1 : pp. 1–10
Abstract
Let $α$ be a flow on a Banach algebra $\mathcal{B}$, and $t → u_t$ a continuous function from $\boldsymbol{R}$ into the group of invertible elements of $\mathcal{B}$ such that $u_sα_s(u_t) = u_{s+t}, s, t ∈ \boldsymbol{R}$. Then $β_t$ = Ad$u_t ◦ α_t$, $t ∈ \boldsymbol{R}$ is also a flow on $\mathcal{B}$, where Ad$u_t(B) \triangleq u_tBu^{−1}_t$ for any $B ∈ \mathcal{B}$. $β$ 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), then $β$ is a cocycle perturbation of $α$. And the flows on a nest algebra (or quasi-triangular algebra) are all uniformly continuous.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2014-CMR-18982
Communications in Mathematical Research , Vol. 30 (2014), Iss. 1 : pp. 1–10
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: cocycle perturbation inner perturbation nest algebra quasi-triangular algebra.