Abstract
Let and be the families of operator monotone functions on satisfying , where and are continuous and is increasing. Suppose and are the corresponding operator connections. We will show that if A, then and are both increasing for , and then we will apply this to the geometric operator means to get a simple assertion from which many operator inequalities follow.
Citation
Mitsuru UCHIYAMA. "Criteria for monotonicity of operator means." J. Math. Soc. Japan 55 (1) 197 - 207, January, 2003. https://doi.org/10.2969/jmsj/1196890849
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