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The perturbation semigroup was first defined in the case of $*$-algebras byChamseddine, Connes and van Suijlekom. In this paper, we take $\mathcal{E}$ asa concrete operator system with unit. We first give a definition of gauge group$\mathcal{G}(\mathcal{E})$ of $\mathcal{E}$, after that we give the definitionof perturbation semigroup of $\mathcal{E}$, and the closed perturbationsemigroup of $\mathcal{E}$ with respect to the Haagerup tensor norm. We alsoshow that there is a continuous semigroup homomorphism from the closedperturbation semigroup to the collection of unital completely bounded Hermitianmaps over $\mathcal{E}$. Finally we compute the gauge group and perturbationsemigroup of the Toeplitz system as an example.

The Gauge Group and Perturbation Semigroup of an Operator System