### Citations

362 |
Operator Spaces
- Effros, Ruan
- 2000
(Show Context)
Citation Context ...entation and Schreiner’s matrix regular operator space to the duality. Usually, an operator system means a unital involutive subspace of BpHq or its abstract characterization given by Choi and Effros =-=[CE]-=-, but here we follow Werner’s terminology. In this paper, a (nonunital) operator system means a matrix ordered operator space which is completely isomorphic and complete order isomorphic to an involut... |

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

175 |
An Invitation to C∗-Algebra
- Arveson
- 1981
(Show Context)
Citation Context ... q with }F }MnpV qs1. By [P, Lemma 8.1], the linear map ϕ : X ÑM2n defined by ϕp λIH x y µIH q λIn F Φpxq F Φpyq µIn is a unital completely positive map. By Arveson’s extension theorem =-=[A]-=-, ϕ has a unital completely positive extension ψ :M2pW q CIH ` CIH ÑM2n. The linear map θ : x P W ÞÑ x x x x 1 1 x 1 1 P M2pW q is completely positive. We write ψ θ ϕ1 F Φ F Φ ... |

37 |
Injectivity and decomposition of completely bounded maps
- Haagerup
- 1985
(Show Context)
Citation Context ...R SPACE AND OPERATOR SYSTEM 5 Proof. We first define }x}reg inftmaxt}a}n, }d}nu : a x x d PM2npV q u, x PMnpV q. Note that this definition is similar to the norm } }dec of a decomposable map =-=[Ha]-=-. The set which we take an infimum over is not empty and we have }x}reg ¤ K}x}n. Multiplying both sides by the scalar matrix 1 0 0 1 , we see that a x x d PM 2n if and only if a 0 0 d ¤ 0... |

13 | Tensor Products of Operator Systems - Kavruk, Paulsen, et al. - 2011 |

7 |
Matrix regular operator spaces
- Schreiner
- 1998
(Show Context)
Citation Context ...ubspace of BpHq or its abstract characterization given by Werner [W]. For a matrix ordered operator space V with complete norm, V is matrix regular if and only if its dual space V is matrix regular =-=[S2]-=-. The category of (nonunital) operator systems contains the class of C-algebras and Haagerup’s noncommutative Lp-spaces [H]. The category of matrix regular operator spaces contains the class of C-al... |

4 | Ordered involutive operator spaces, Positivity 11 - Blecher, Kirkpatrick, et al. |

4 |
Corrigendum to the paper: “Adjoining an order unit to a matrix ordered space”, Positivity 11
- Karn
(Show Context)
Citation Context ...tains the class of C-algebras and their duals, preduals of von Neumann algebras, and the Schatten class Sp [S1]. Karn proved that every matrix regular operator space is a (nonunital) operator system =-=[K]-=-. Since the dual space of a matrix regular operator space is matrix regular, the dual space of a matrix regular operator space is also a (nonunital) operator system. Its converse would be reasonable i... |

2 |
Subspaces of LpHq that are -invariant
- Werner
(Show Context)
Citation Context ...) operator system means a matrix ordered operator space which is completely isomorphic and complete order isomorphic to an involutive subspace of BpHq or its abstract characterization given by Werner =-=[W]-=-. For a matrix ordered operator space V with complete norm, V is matrix regular if and only if its dual space V is matrix regular [S2]. The category of (nonunital) operator systems contains the clas... |

1 |
Noncommutative Lp-space and operator system
- Han
(Show Context)
Citation Context ...m, V is matrix regular if and only if its dual space V is matrix regular [S2]. The category of (nonunital) operator systems contains the class of C-algebras and Haagerup’s noncommutative Lp-spaces =-=[H]-=-. The category of matrix regular operator spaces contains the class of C-algebras and their duals, preduals of von Neumann algebras, and the Schatten class Sp [S1]. Karn proved that every matrix regu... |

1 |
Matrix Regular Orders on Operator Spaces
- Schreiner
- 1995
(Show Context)
Citation Context ... Haagerup’s noncommutative Lp-spaces [H]. The category of matrix regular operator spaces contains the class of C-algebras and their duals, preduals of von Neumann algebras, and the Schatten class Sp =-=[S1]-=-. Karn proved that every matrix regular operator space is a (nonunital) operator system [K]. Since the dual space of a matrix regular operator space is matrix regular, the dual space of a matrix regul... |