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| 摘要: |
| 本文利用Mond-Pečarić方法对凸函数的n个算子凸性进行了比式估计.在此基础上,得到了n个代数平均的幂与n个算子的幂的代数平均的比较,n个算子的几何平均的幂与n个算子的幂的几何平均的比较.特别地,文中还给出了代数平均和混序几何平均. |
| 关键词: 算子凸 代数平均 几何平均 混序几何平均 |
| DOI： |
| 分类号:O177.1 |
| 基金项目:Partially Supported by NSFC (10471085);the Basic Science and Technological Frontier Project of Henan Province (132300410261). |
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| BOUNDEDNESS OF OPERATOR CONVEXITY FOR CONVEX FUNCTIONS AND APPLICATIONS FOR OPERATOR MEANS |
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ZUO Hong-liang,DUAN Guang-cai
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| Abstract: |
| In this paper, we estimate boundedness of operator convexity for convex functions. As an application, we obtain some relations between the power of operator means (arithmetic mean, geometric mean, chaotically geometric mean) and those means of operator powers. In particular, we obtain the order relation between arithmetic mean and chaotically geometric mean. |
| Key words: operator convex arithmetic mean geometric mean chaotically geometric mean |
