For an n-tuple of positive invertible operators on a Hilbert space, we present some variants of Ando–Hiai type inequalities for deformed means from an n-variable operator mean by an operator mean, which is related to the information monotonicity of a certain unital positive linear map. As an application, we investigate the monotonicity of the power mean from the deformed mean in terms of the generalized Kantorovich constants under the operator order. Moreover, we improve the norm inequality for the operator power means related to the Log-Euclidean mean in terms of the Specht ratio.

中文翻译：

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变形方法和应用的 ANDO-HIAI 型不等式的变体

为n-希尔伯特空间上的正可逆算子元组，我们提出了变形均值的 Ando-Hiai 型不等式的一些变体n-变量算子均值由一个算子均值组成，它与某个单位正线性图的信息单调性有关。作为一个应用，我们根据算子阶下的广义 Kantorovich 常数研究变形均值的幂均值的单调性。此外，我们在 Specht 比率方面改进了与对数欧几里得均值相关的算子功率均值的范数不等式。