The Gauge Group and Perturbation Semigroup of an Operator System
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 perturbatio...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2022 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2022
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211727 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Gauge Group and Perturbation Semigroup of an Operator System. Rui Dong. SIGMA 18 (2022), 060, 18 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862734656393183232 |
|---|---|
| author | Dong, Rui |
| author_facet | Dong, Rui |
| citation_txt | The Gauge Group and Perturbation Semigroup of an Operator System. Rui Dong. SIGMA 18 (2022), 060, 18 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2026-04-17T16:10:00Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211727 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T16:10:00Z |
| publishDate | 2022 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Dong, Rui 2026-01-09T12:53:24Z 2022 The Gauge Group and Perturbation Semigroup of an Operator System. Rui Dong. SIGMA 18 (2022), 060, 18 pages 1815-0659 2020 Mathematics Subject Classification: 46L07; 47L25; 58B34; 11M55 arXiv:2111.13076 https://nasplib.isofts.kiev.ua/handle/123456789/211727 https://doi.org/10.3842/SIGMA.2022.060 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. The author wishes to express his gratitude to Walter van Suijlekom from Radboud University Nijmegen for stimulating discussions on related topics. Besides that, the author would like to thank all the anonymous referees for their significant suggestions, which improved the quality of this paper a lot. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Gauge Group and Perturbation Semigroup of an Operator System Article published earlier |
| spellingShingle | The Gauge Group and Perturbation Semigroup of an Operator System Dong, Rui |
| title | The Gauge Group and Perturbation Semigroup of an Operator System |
| title_full | The Gauge Group and Perturbation Semigroup of an Operator System |
| title_fullStr | The Gauge Group and Perturbation Semigroup of an Operator System |
| title_full_unstemmed | The Gauge Group and Perturbation Semigroup of an Operator System |
| title_short | The Gauge Group and Perturbation Semigroup of an Operator System |
| title_sort | gauge group and perturbation semigroup of an operator system |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211727 |
| work_keys_str_mv | AT dongrui thegaugegroupandperturbationsemigroupofanoperatorsystem AT dongrui gaugegroupandperturbationsemigroupofanoperatorsystem |