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## On maximal tensor products and quotient maps of operator systems

Venue: | J. Math. Anal. Appl |

Citations: | 4 - 1 self |

### Citations

510 | JB: A Course in Functional Analysis - Conway - 1990 |

362 |
Operator Spaces
- Effros, Ruan
- 2000
(Show Context)
Citation Context ...spaces of a real continuous function algebra on a compact set [Ka]. As for its noncommutative counterpart, Choi and Effros gave an abstract characterization of the unital involutive subspaces of BpHq =-=[CE]-=-. The former is called a real function system or a real ordered vector space with an Archimedean order unit while the latter is termed an operator system. Ever since the work by Choi and Effros, the n... |

239 | Completely bounded maps and operator algebras, Cambridge - Paulsen - 2002 |

137 | Compact Convex Sets and Boundary Integrals, Springer-Verlag - Alfsen - 1971 |

41 |
A representation theory for commutative topological algebra
- Kadison
- 1951
(Show Context)
Citation Context ...roduct and establish the duality between quotient maps and complete order embeddings. 1. Introduction Kadison characterized the unital subspaces of a real continuous function algebra on a compact set =-=[Ka]-=-. As for its noncommutative counterpart, Choi and Effros gave an abstract characterization of the unital involutive subspaces of BpHq [CE]. The former is called a real function system or a real ordere... |

39 |
On nuclear C∗-algebras
- Lance
- 1973
(Show Context)
Citation Context ... this paper, we continue to study the tensor products in [KPTT1] and the quotients in [KPTT2]. With the same spirit as in [HP], we give a simple and generalized proof of the classical Lance’s theorem =-=[L1, L2]-=-. In section 3, we introduce the notion of complete order quotient maps which can be regarded as quotient maps in the category of operator systems and show that the maximal tensor product is projectiv... |

21 | Vector spaces with an order unit
- Paulsen, Tomforde
(Show Context)
Citation Context ...f C-algebras. Recently, the fundamental and systematic developments in the theory of operator systems have been carried out through a series of papers [PT, PTT, KPTT1, KPTT2]. Perhaps, the reference =-=[PT]-=- is the cornerstone for this program. Under the naive definition of the quotient and that of the tensor product of real function systems, the order unit sometimes fails to be Archimedean. See for exam... |

16 | Operator system structures on ordered spaces
- Paulsen, Todorov, et al.
(Show Context)
Citation Context ...ced in [PT] helps remedy this problem. In order to apply this idea to the noncommutative situation, the Archimedeanization of a matrix ordered -vector space with a matrix order unit is introduced in =-=[PTT]-=-. Based on the matricial Archimedeanization process, the tensor products and the quotients of operator systems are defined and studied in [KPTT1] and [KPTT2] respectively. Based on these developments,... |

13 | Tensor Products of Operator Systems
- Kavruk, Paulsen, et al.
- 2011
(Show Context)
Citation Context ...-vector space with a matrix order unit is introduced in [PTT]. Based on the matricial Archimedeanization process, the tensor products and the quotients of operator systems are defined and studied in =-=[KPTT1]-=- and [KPTT2] respectively. Based on these developments, a simple and generalized proof of the celebrated ChoiEffros-Kirchberg approximation theorem for nuclear C-algebras has been given in [HP]. In t... |

13 | C ∗ -algebras generated by operator systems - Kirchberg, Wassermann - 1998 |

4 | An approximation theorem for nuclear operator systems
- Han, Paulsen
- 2011
(Show Context)
Citation Context ...in [KPTT1] and [KPTT2] respectively. Based on these developments, a simple and generalized proof of the celebrated ChoiEffros-Kirchberg approximation theorem for nuclear C-algebras has been given in =-=[HP]-=-. In this paper, we continue to study the tensor products in [KPTT1] and the quotients in [KPTT2]. With the same spirit as in [HP], we give a simple and generalized proof of the classical Lance’s theo... |

4 | Corrigendum to the paper: “Adjoining an order unit to a matrix ordered space”, Positivity 11 - Karn |

3 |
Tensor products and nuclear C-algebras, Operator algebras and applications, Part I
- Lance
- 1980
(Show Context)
Citation Context ... this paper, we continue to study the tensor products in [KPTT1] and the quotients in [KPTT2]. With the same spirit as in [HP], we give a simple and generalized proof of the classical Lance’s theorem =-=[L1, L2]-=-. In section 3, we introduce the notion of complete order quotient maps which can be regarded as quotient maps in the category of operator systems and show that the maximal tensor product is projectiv... |

2 |
Quotients, exactness and WEP in the operator systems category, preprint
- Kavruk, Paulsen, et al.
(Show Context)
Citation Context ...ce with a matrix order unit is introduced in [PTT]. Based on the matricial Archimedeanization process, the tensor products and the quotients of operator systems are defined and studied in [KPTT1] and =-=[KPTT2]-=- respectively. Based on these developments, a simple and generalized proof of the celebrated ChoiEffros-Kirchberg approximation theorem for nuclear C-algebras has been given in [HP]. In this paper, w... |

2 |
Subspaces of LpHq that are -invariant
- Werner
(Show Context)
Citation Context ...n by the standard dual of operator spaces. To get rid of the finite dimensional assumption and to reflect the operator space dual norm, we apply Werner’s unitization of matrix ordered operator spaces =-=[W]-=- to the dual spaces of operator systems. We consider the completely positive maps associated with the maximal tensor products and prove their factorization property in section 5. Finally, we establish... |

1 | Matrix regular operator space and operator system - Han |