INDUCTIVE LIMIT IN THE CATEGORY OF C*-TERNARY RINGS
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We show the existence of inductive limit in the category of $C^{\ast}$-ternary rings. It is proved that the inductive limit of $C^{\ast}$-ternary rings commutes with the functor $\mathcal{A}$ in the sense that if $(M_n, \phi_n)$ is an inductive system of $C^{\ast}$-ternary rings, then $\varinjlim \mathcal{A}(M_n)=\mathcal{A}(\varinjlim M_n)$. Some local properties (such as nuclearity, exactness and simplicity) of inductive limit of $C^{\ast}$-ternary rings have been investigated. Finally we obtain $\varinjlim M_n^{\ast\ast}=(\varinjlim M_n)^{\ast\ast}$.
Abstract
We show the existence of inductive limit in the category of $C^{\ast}$-ternary rings. It is proved that the inductive limit of $C^{\ast}$-ternary rings commutes with the functor $\mathcal{A}$ in the sense that if $(M_n, \phi_n)$ is an inductive system of $C^{\ast}$-ternary rings, then $\varinjlim \mathcal{A}(M_n)=\mathcal{A}(\varinjlim M_n)$. Some local properties (such as nuclearity, exactness and simplicity) of inductive limit of $C^{\ast}$-ternary rings have been investigated. Finally we obtain $\varinjlim M_n^{\ast\ast}=(\varinjlim M_n)^{\ast\ast}$.
참고문헌 (13)
- F. Abadie and D. Ferraro, "Applications of ternary rings to C*-algebras", Adv. Oper. Theory, 2(3), pp.293~317 (2017)[DOI]
- Janson Antony, "Operator space tensor products and inductive limits", Journal of Mathematical Analysis and Applications, 470(1), pp.235~250 (2019), Elsevier BV[DOI]
- Dennis Bohle, "A K-theoretic approach to the classification of symmetric spaces", Journal of Pure and Applied Algebra, 219(10), pp.4295~4321 (2015), Elsevier BV[DOI]
- Edward G. Effros, "On injectivity and nuclearity for operator spaces", Duke Mathematical Journal, 110(3) (2001), Duke University Press[DOI]
- M. Hamana, "Injective envelopes of dynamical systems, in Operator algebras and operator theory (Craiova, 1989)", Pitman Res. Notes Math. Ser, 271, pp.69~77 (1992), Longman Sci. Tech
- T. Ho, "TERNARY WEAKLY AMENABLE C*-ALGEBRAS AND JB*-TRIPLES", The Quarterly Journal of Mathematics, 64(4), pp.1109~1139 (2012), Oxford University Press (OUP)[DOI]
- Arpit Kansal, "Inductive limit in the category of TRO", Annals of Functional Analysis, 11(3), pp.748~760 (2020), Springer Science and Business Media LLC[DOI]
- Manmohan Kaur, "Local Properties of Ternary Rings of Operators and Their Linking C *-Algebras", Journal of Functional Analysis, 195(2), pp.262~305 (2002), Elsevier BV[DOI]
- E. M. Landesman, "The second dual of a C*-ternary ring", Canadian Mathematical Bulletin, 26(2), pp.241~246 (1983), Canadian Mathematical Society[DOI]
- M. A. Naimark, "Normed Algebras" (1972), Wolters-Noordhoff Publishing
- Robert Pluta, "Ternary operator categories", Journal of Mathematical Analysis and Applications, 505(2), pp.125590~ (2022), Elsevier BV[DOI]
- M. Rordam, "An Introduction to K-theory for C* Algebras" (2000), Cambridge University Press
- Heinrich Zettl, "A characterization of ternary rings of operators", Advances in Mathematics, 48(2), pp.117~143 (1983), Elsevier BV[DOI]