#### DMCA

## real-time systems (1994)

Venue: | In the 14th IEEE International Conference on Distributed Computing Systems (OPODIS94 |

Citations: | 6 - 0 self |

### Citations

361 |
Operator Spaces,
- Effros, Ruan
- 2000
(Show Context)
Citation Context ...in the C˚-algebra category: every C˚-algebra is a C˚- quotient of C˚pFq and a C˚-subalgebra of BpHq for suitable choices of F and H . Every operator system is a quotient of CI and a subsystem of BpHq =-=[CE]-=- for suitable choices of I and H . We will prove a Kirchberg type tensor theorem CI bmin BpHq “ CI bmax BpHq. The proof is independent of Kirchberg’s theorem. Combining this with Kavruk’s idea [K], we... |

210 | Introduction to Operator Space Theory - Pisier - 2003 |

203 | C*-algebras and Finite-dimensional Approximations. Graduate studies in mathematics - Brown, Ozawa - 2008 |

49 | The standard dual of an operator space - Blecher - 1992 |

32 |
Commutants of unitaries in UHF algebras and functorial properties of exactness
- Kirchberg
- 1994
(Show Context)
Citation Context ...Hq [CE] for suitable choices of I and H . We will prove a Kirchberg type tensor theorem CI bmin BpHq “ CI bmax BpHq. The proof is independent of Kirchberg’s theorem. Combining this with Kavruk’s idea =-=[K]-=-, we give a new operator system theoretic proof of Kirchberg’s theorem. We also prove that the operator system analogue CI bmin CI “ CI bc CI of Kirchberg’s conjecture C˚pFqb̂minC˚pFq “ C˚pFqb̂maxC˚pF... |

24 |
Topics in Geometric Group Theory,
- Harpe
- 2000
(Show Context)
Citation Context ...K]. Since ℓ28 ‘1 ℓ38 Ă C˚pZ2 ˚ Z3q contains enough unitaries, we have C˚pZ2 ˚ Z3q bmin BpHq “ C˚pZ2 ˚ Z3q bmax BpHq by [KPTT2, Proposition 9.5]. The free group F8 embeds into the free product Z2 ˚ Z3 =-=[LH]-=-. By [P2, Proposition 8.8], C˚pF8q is a C˚-subalgebra of C˚pZ2 ˚Z3q complemented by a unital completely positive map. A KIRCHBERG TYPE TENSOR THEOREM FOR OPERATOR SYSTEMS 11 The following proof is m... |

23 |
Lifling problems and local reflexivity for C∗-algebras
- Effros, Haagerup
- 1985
(Show Context)
Citation Context ...uotients [PT]. Even though some perturbation is allowed, we will see that there is a certain rigidity. Finally, we present an operator system theoretic approach to the Effros-Haagerup lifting theorem =-=[EH]-=-. 2. Preliminaries Given an operator system S, we call J Ă S the kernel, provided that it is the kernel of a unital completely positive map from S to another operator system. If we define a family of ... |

21 | Free products of completely positive maps and spectral sets - Boca - 1991 |

21 | Vector spaces with an order unit
- Paulsen, Tomforde
(Show Context)
Citation Context ...: CI Ñ S? The answer is negative in an extreme manner. An operator system satisfying such a lifting property is necessarily one-dimensional. This is essentially due to Archimedeanization of quotients =-=[PT]-=-. Even though some perturbation is allowed, we will see that there is a certain rigidity. Finally, we present an operator system theoretic approach to the Effros-Haagerup lifting theorem [EH]. 2. Prel... |

20 |
A simple proof of a theorem of Kirchberg and related results on
- Pisier
- 1996
(Show Context)
Citation Context ...berg’s theorem. This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2012R1A1A1012190). 1 2 KYUNG HOON HAN The proof was later simplified in =-=[P1]-=- and [FP] using operator space theory and operator system theory, respectively. Kirchberg’s theorem is striking if we recall that C˚pFq and BpHq are universal objects in the C˚-algebra category: every... |

18 | On Gromov–Hausdorff convergence for operator metric spaces - Kerr, Li |

16 | Operator system structures on ordered spaces
- Paulsen, Todorov, et al.
(Show Context)
Citation Context ... cone in R3 generated by tpx, y, 1q : px ´ 1q2 ` y2 ď 1, y ě 0u and the origin. The triple V :“ pC3, V `, p1, 1, 2qq is an Archimedean ordered ˚-vector space. The operator system quotient of OMAXpV q =-=[PTT]-=- by the z-axis is ℓ28. Suppose that dimS ě 2. Let v be a positive element in S distinct from the scalar multiple of the identity. Considering v ´ λI for sufficiently large λ ą 0, we may assume that th... |

15 |
Operator system quotients of matrix algebras and their tensor products
- Farenick, Paulsen
- 2012
(Show Context)
Citation Context ...eorem. This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2012R1A1A1012190). 1 2 KYUNG HOON HAN The proof was later simplified in [P1] and =-=[FP]-=- using operator space theory and operator system theory, respectively. Kirchberg’s theorem is striking if we recall that C˚pFq and BpHq are universal objects in the C˚-algebra category: every C˚-algeb... |

13 | Tensor Products of Operator Systems
- Kavruk, Paulsen, et al.
- 2011
(Show Context)
Citation Context ...S, the following are equivalent [KPTT2, Theorem 7.6]: (i) S has the double commutant expectation property; (ii) S is pel, cq-nuclear; 4 KYUNG HOON HAN (iii) S bmin C˚pF8q “ S bmax C˚pF8q. We refer to =-=[KPTT1]-=- and [KPTT2] for general information on tensor products and quotients of operator systems. 3. A Kirchberg type tensor theorem for operator systems Suppose that I is an index set and tIkukPN is a seque... |

9 | Operator system structures on the unital direct sum of C*-algebras, arXiv:1011.1247
- Fritz
- 2010
(Show Context)
Citation Context ...e have the complete order embeddings Cιk ‘1 Cι1l ĂMkpCpr0, 1sqqιk ‘1 MkpCpr0, 1sqqι1l ĂMkpCpr0, 1sqqιk ˚MkpCpr0, 1sqqι1l Ă ˚kPN,ιkPIkMkpCpr0, 1sqιk. The coproduct of two operator systems studied in =-=[F]-=- can be generalized to the coproduct of a finite family of operator systems in an obvious way. We now define the coproduct of arbitrary family of operator systems to prove the lifting property of CI .... |

6 | C∗-algebras with the weak expectation property and a multivariable analogue of Ando’s theorem on the numerical radius - Farenick, Kavruk, et al. |

6 | The weak expectation property and Riesz interpolation, arXiv 1201.5414
- Kavruk
(Show Context)
Citation Context ...Hq [CE] for suitable choices of I and H . We will prove a Kirchberg type tensor theorem CI bmin BpHq “ CI bmax BpHq. The proof is independent of Kirchberg’s theorem. Combining this with Kavruk’s idea =-=[K]-=-, we give a new operator system theoretic proof of Kirchberg’s theorem. We also prove that the operator system analogue CI bmin CI “ CI bc CI of Kirchberg’s conjecture C˚pFqb̂minC˚pFq “ C˚pFqb̂maxC˚pF... |

4 | On maximal tensor products and quotient maps of operator systems - Han |

4 | An approximation theorem for nuclear operator systems - Han, Paulsen - 2011 |

2 | Tensor Norms and Opeator - Defant, Floret - 1993 |

2 |
Quotients, exactness and WEP in the operator systems category, preprint
- Kavruk, Paulsen, et al.
(Show Context)
Citation Context ...wing are equivalent [KPTT2, Theorem 7.6]: (i) S has the double commutant expectation property; (ii) S is pel, cq-nuclear; 4 KYUNG HOON HAN (iii) S bmin C˚pF8q “ S bmax C˚pF8q. We refer to [KPTT1] and =-=[KPTT2]-=- for general information on tensor products and quotients of operator systems. 3. A Kirchberg type tensor theorem for operator systems Suppose that I is an index set and tIkukPN is a sequence of index... |

1 | Operator systems from discrete groups Comm - Farenick, Kavruk, et al. |