First, that prime C~* -algebras with countable primitive ideals are all primitive C*-algebras is proved. Then the proof that prime C~* -algebras with property RR(A) = 0 are all primitive C~*-algebras is given.
In this paper, we discussed some improtant inequalities, such as young inequality, Holder inequality and Minkowski inequality,about the positive elements in C~*-Algebra.
This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. ...This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. That is to say we have not only defined some relevant new concept,but also obtained some results about them.展开更多
We introduce a special tracial Rokhlin property for unital C~＊-algebras. Let A be a unital tracial rank zero C~＊-algebra（or tracial rank no more than one C~＊-algebra）. Suppose that α ： G → Aut（A） is an actio...We introduce a special tracial Rokhlin property for unital C~＊-algebras. Let A be a unital tracial rank zero C~＊-algebra（or tracial rank no more than one C~＊-algebra）. Suppose that α ： G → Aut（A） is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~＊-algebra. Then, the crossed product C~＊-algebra C~＊（G, A, α） has tracia rank zero（or has tracial rank no more than one）. In fact,we get a more general results.展开更多
Let A be a unital simple C-algebra of real rank zero,stable rank one,with weakly unperforated K<sub>0</sub>（A）and unique normalized quasi-trace τ,and let X be a compact metric space.We show that two mon...Let A be a unital simple C-algebra of real rank zero,stable rank one,with weakly unperforated K<sub>0</sub>（A）and unique normalized quasi-trace τ,and let X be a compact metric space.We show that two monomorphisms Φ,Ψ:C（X）→A are approximately unitarily equivalent if and only if Φ and Ψ induce the same element in KL（C（X）,A）and the two linear functionals τ ο Φ and τ ο Φ are equal.We also show that,with an injectivity condition,an almost multiplicative morphism from C（X） into A with vanishing KK-obstacle is close to a homomorphism.展开更多
In this paper,we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen's equations in Banach modules over a unital C~*-algebra.It is applied to show the stability of universal Jensen's equatio...In this paper,we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen's equations in Banach modules over a unital C~*-algebra.It is applied to show the stability of universal Jensen's equations in a Hilbert module over a unital C~*-algebra.Moreover,we prove the stability of linear operators in a Hilbert module over a unitat C~*-algebra.展开更多
The relation between the inseparable prime C*-algebras and primitive C*-algebras is studied, and we prove that prime AW*-algebras are all primitive C*-algebras.
Let E be a countably generated Hilbert module over a C~*-algebra A and B(E) the set ofall bounded module maps on E. We find that B(E) is isometric isomorphic onto the leftmultipliers of K(E), where K(E) is the "c...Let E be a countably generated Hilbert module over a C~*-algebra A and B(E) the set ofall bounded module maps on E. We find that B(E) is isometric isomorphic onto the leftmultipliers of K(E), where K(E) is the "compact" module maps on E. In the case that A isinfinitely dimensional primitive C~*-algebra, E is shown to be self-dual if and only if E isalgebraically finitely generated.展开更多
文摘First, that prime C~* -algebras with countable primitive ideals are all primitive C*-algebras is proved. Then the proof that prime C~* -algebras with property RR(A) = 0 are all primitive C~*-algebras is given.
文摘In this paper, we discussed some improtant inequalities, such as young inequality, Holder inequality and Minkowski inequality,about the positive elements in C~*-Algebra.
文摘This paper,combined algebraical structure with analytical system,has studied the part of theory of C~*-modules over A by using the homolgical methods, where A is a commutative C~*-algebra over complex number field C. That is to say we have not only defined some relevant new concept,but also obtained some results about them.
文摘We introduce a special tracial Rokhlin property for unital C~＊-algebras. Let A be a unital tracial rank zero C~＊-algebra（or tracial rank no more than one C~＊-algebra）. Suppose that α ： G → Aut（A） is an action of a finite group G on A, which has this special tracial Rokhlin property, and suppose that A is a α-simple C~＊-algebra. Then, the crossed product C~＊-algebra C~＊（G, A, α） has tracia rank zero（or has tracial rank no more than one）. In fact,we get a more general results.
基金Research partially supported by NSF Grants DMS 93-01082(H.L)and DMS-9401515(G.G)This work was reported by the first named author at West Coast Operator Algebras Seminar(Sept.1995,Eugene,Oregon)
文摘Let A be a unital simple C-algebra of real rank zero,stable rank one,with weakly unperforated K<sub>0</sub>（A）and unique normalized quasi-trace τ,and let X be a compact metric space.We show that two monomorphisms Φ,Ψ:C（X）→A are approximately unitarily equivalent if and only if Φ and Ψ induce the same element in KL（C（X）,A）and the two linear functionals τ ο Φ and τ ο Φ are equal.We also show that,with an injectivity condition,an almost multiplicative morphism from C（X） into A with vanishing KK-obstacle is close to a homomorphism.
基金supported by Korea Research Foundation Grant KRF-2002-041-C00014
文摘In this paper,we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen's equations in Banach modules over a unital C~*-algebra.It is applied to show the stability of universal Jensen's equations in a Hilbert module over a unital C~*-algebra.Moreover,we prove the stability of linear operators in a Hilbert module over a unitat C~*-algebra.
文摘The relation between the inseparable prime C*-algebras and primitive C*-algebras is studied, and we prove that prime AW*-algebras are all primitive C*-algebras.
基金Project partially supported by the National Natural Science Foundation of China.
文摘Let E be a countably generated Hilbert module over a C~*-algebra A and B(E) the set ofall bounded module maps on E. We find that B(E) is isometric isomorphic onto the leftmultipliers of K(E), where K(E) is the "compact" module maps on E. In the case that A isinfinitely dimensional primitive C~*-algebra, E is shown to be self-dual if and only if E isalgebraically finitely generated.
