Comparison of Various Means for Operators
Comparison of Various Means for Operators
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各种操作手段的比较
DOI：
10.1006/jfan.1998.3375
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发表时间：
1999
影响因子：
1.7
通讯作者：
H. Kosaki
中科院分区：
文献类型：
--
作者：
F. Hiai;H. Kosaki
对于希尔伯特空间算子H,K,X和H,K⩾0，范数不等式|||H1/2XK1/2|||⩽12|||HX+XK|||已知，其中 |||·|||是任意酉不变范数。研究了这种算术几何平均不等式的改进。对于算子的各种自然方法（例如对数平均值）确实建立了类似的范数不等式。
For Hilbert space operatorsH,K,XwithH,K⩾0 the norm inequality |||H1/2XK1/2|||⩽12|||HX+XK||| is known, where |||·||| is an arbitrary unitarily invariant norm. A refinement of this arithmetic–geometric mean inequality is studied. Similar norm inequalities are indeed established for various natural means for operators such as the logarithmic mean.