Some Properties Of Matrix Trace On Mn(A)

In this article, we study some properties of the matrix traces on C*-algebras. It contains four chapters.In Chapter1, we introduce the background and basic definitions of this article.In Chapter2, we introduce the matrix traces on C*-algebras and their basic proper-ties. Then we discuss the existence of nonzero matrix traces.In Chapter3. we discuss the uniqueness of condition expectations to lift a matrix trace; we obtain the formula of matrix traces with condition expectation lifting; we prove a trace inequality for trace-type linear maps on Mn(C), and also give an example to indicate that a trace inequality may be false for trace-type linear maps on Mn(C).In Chapter4, we discuss some properties for matrix traces on commutative C*-algebras. We generalize some results of Bellman to matrix trace case. We also give an estimation for the norm of a matrix trace on commutative C*-algebras.