C~*-代数交换性的算子凸函数特征

On characterizations of communtativity of C~*-algebras

考虑了C* -代数A交换性的凸函数特征.构造了在C* -代数A上是凸函数,但是在M2 上却不是算子凸的函数.并由算子凸函数的性质证明了非线性型的Strinespring定理,即C*

The characterizations for convex function of commutativity of a C~*-algebra A is taken into account.some functions which are not matrix convex of order 2 but operator convex on A is constructed From operator convex property of functions, we give the result as the nonlinear version of Strinespring theorem. That is, a C~*-algebra A is commutative if and only if there exists a continuous convex function which is not matrix convex on M_2 but operator convex on a C~*- algebra A.