The Gauge Group and Perturbation Semigroup of an Operator System - Dong, Rui (Symmetry, Integrability and Geometry: Methods and Applications, 2022)
The perturbation semigroup was first defined in the case of ∗-algebras by Chamseddine, Connes, and van Suijlekom. In this paper, we take as a concrete operator system with a unit. We first define the gauge group () of . After that, we define the perturbation semigroup of and the closed perturbation semigroup of E with respect to the Haagerup tensor norm. We also show that there is a continuous semigroup homomorphism from the closed perturbation semigroup to the collection of unital completely bounded Hermitian maps over . Finally, we compute the gauge group and perturbation semigroup of the Toeplitz system as an example.