Research On Bellman Inequalities In Several Different Settings

Bellman inequalities of matrix trace and operator trace, Bellman inequalities of generalized matrix trace in C* -algebra are studied, and some relatable inequalities are talked about.This thesis consists three chapters.Chapter l:Bellman inequalities of matrix trace and some relatable inequalities are studied. The inequalityTr[(AB}]k B are semidefmite positive Hermit matrix is proved, consequently one open questions of Bellman is answered.In addition, the inequalityTr((AB}m) < {Tr(A2m)Tr(B2m)}1/2for A,B∈Mn(C) are semidefmite positive matrix and m∈AMsproved, another open questions of Bellman is answered.Chapters 2: The Bellman question is extended to arbitrary Hilbert space, the inequalityfor A∈T(H), n∈N is proved. In addition, the inequalityTr((AB)2n)