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( Ak Bk) ,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:M n(C(Ω))→C(Ω ) is introduced, Bellman inequality on generalized matrix trace τ is studied.The following inequality is proved:τ((AB) k)≤τ(A kB k),where A,B are positive elements in a unital C * algebra M n(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.
出处
《纺织高校基础科学学报》
CAS
2002年第2期132-134,共3页
Basic Sciences Journal of Textile Universities
