Some Inequalities about the Positive Elements in C~*-Algebra

In this paper, we discussed some improtant inequalities, such as young inequality, Holder inequality and Minkowski inequality,about the positive elements in C~*-Algebra.

An Introduction to the Theory of C~*-modules

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.

保持因子交换性的可加映射

设x和y是代数中的两个元．如果存在某个数ξ，使得xy=ξyx，称x和y关于因子ξ交换．给出了标准算子代数间双边保关于因子交换的可加满射的刻画和分类以及C^＊-代数间保关于因子交换的有界线性满射的刻画和分类．

CROSSED PRODUCTS BY FINITE GROUP ACTIONS WITH CERTAIN TRACIAL ROKHLIN PROPERTY

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.

Proof of inseparable prime C~*-algebras A with RR(A)=0 being primitive C~*-algebras

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.

Classification of Homomorphisms from C(X)to Simple C~*-Algebras of Real Rank Zero

Let A be a unital simple C-algebra of real rank zero,stable rank one,with weakly unperforated K0（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.

内射C^＊—代数

本文对内射 C~*-代数作了进一步讨论,给出了内射 C~*-代数的子代数是内射的一个充分条件与内射 C~*-代数的某些结果。

Universal Jensen's Equations in Banach Modules over a C-Algebra and Its Unitary Group

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.

HILBERT C~*-MODULES AND THEIR BOUNDED MODULE MAPS

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.

On Monotone Product of Operator Algebras

In this note, we give complete descriptions of the structure of the monotone product of two yon Neumann algebras and two C^＊-algebras. We show that the monotone product of two simple yon Neumann algebras and C^＊-algebras aren＇t simple again. We also show that the monotone product of two hyperfinite yon Neumann algebras is again hyperfinite and determine the type of the monotone product of two factors.