@Article{CMR-30-1,
author = {Shi, Luoyi and Yujing, Wu},
title = {Cocycle Perturbation on Banach Algebras},
journal = {Communications in Mathematical Research },
year = {2014},
volume = {30},
number = {1},
pages = {1--10},
abstract = {<p style="text-align: justify;">Let $α$ be a flow on a Banach algebra&nbsp;$\mathcal{B}$, and $t → u_t$ a continuous function
from&nbsp;$\boldsymbol{R}$&nbsp;into the group of invertible elements of&nbsp;$\mathcal{B}$&nbsp;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.</p>},
issn = {2707-8523},
doi = {https://doi.org/2014-CMR-18982},
url = {https://global-sci.com/article/81733/cocycle-perturbation-on-banach-algebras}
}