Operator Monotone Functions Which Are Defined Implicitly And Operator Inequalities (Applications of Analytic Extensions)
Operator Monotone Functions Which Are Defined Implicitly And Operator Inequalities (Applications of Analytic Extensions)
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隐式定义的算子单调函数和算子不等式（解析扩展的应用）
DOI：
10.1006/jfan.2000.3617
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发表时间：
2000
影响因子：
1.1
通讯作者：
M. Uchiyama
中科院分区：
文献类型：
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作者：
M. Uchiyama
函数 tα (0<α<1) 是 0⩽t<∞ 上的算子单调性。这就是所谓的洛纳-海因茨不等式。然而，迄今为止，具体的算子单调函数的例子还不为人所知。我们将系统地寻找隐式定义的算子单调函数。这项研究是新的，我们的方法似乎很有效。我们实际上会找到一系列算子单调函数，其中包括 tα (0<α<1)。此外，通过构造一参数族算子单调函数，我们将得到许多算子不等式；特别是，我们将扩展Furuta不等式和Ando指数不等式。
The function tα (0<α<1) is operator monotone on 0⩽t<∞. This is known as the Lowner–Heinz inequality. However, not too many examples of concrete operator monotone functions are known so far. We will systematically seek operator monotone functions which are defined implicitly. This investigation is new, and our method seems to be powerful. We will actually find a family of operator monotone functions which includes tα (0<α<1). Moreover, by constructing one-parameter families of operator monotone functions, we will get many operator inequalities; especially, we will extend the Furuta inequality and the exponential inequality of Ando.