广义矩阵迹的贝尔曼不等式

摘要

引入了广义矩阵迹τ:Mn(C(Ω))→C(Ω ) ,讨论了在广义矩阵迹下的贝尔曼不等式.证明了C*-代数 Mn(C(Ω))中任意两个正元A,B及k∈N,有τ((AB)k)≤τ(AkBk),这便在更一般的框架下给出了Bellman 问题的一个肯定回答.同时还利用C*-代数证明了其它一些相关不等式.%A generalized matrix trace τ:Mn(C(Ω))→C(Ω ) is introduced, Bellman inequality on generalized matrix trace τ is studied.The following inequality is proved:τ((AB)k)≤τ(AkBk),where A,B are positive elements in a unital C*-algebra Mn(C(Ω)) and k∈N. This gives a positive answer to Bellman problem in a more general setting. Some related inequalities on it are also proved by using the knowledge of C*-algebra.