The Gauge Group and Perturbation Semigroup of an Operator System

Symmetry Integrability and Geometry-Methods and Applications

article

Rui Dong¹ 

[1] Institute for Mathematics, Astrophysics and Particle Physics, Radboud University Nijmegen

关键词: operator algebras;    operator systems;    functional analysis;    noncommutative geometry.;   

DOI  :  10.3842/SIGMA.2022.060

来源: National Academy of Science of Ukraine

【 摘 要 】

The perturbation semigroup was first defined in the case of $*$-algebras by Chamseddine, Connes and van Suijlekom. In this paper, we take $\mathcal{E}$ as a 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 definition of perturbation semigroup of $\mathcal{E}$, and the closed perturbation semigroup of $\mathcal{E}$ 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 $\mathcal{E}$. Finally we compute the gauge group and perturbation semigroup of the Toeplitz system as an example.

【 授权许可】

Unknown