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Operator means deformed by a fixed point method

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Abstract

By means of a fixed point method we discuss the deformation of two-variable and multivariate operator means of positive definite matrices/operators. It is shown that the deformation of any operator mean in the Kubo–Ando sense becomes again an operator mean in the same sense. The operator means deformed by the weighted power means with two parameters are particularly examined.

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Acknowledgements

The author is grateful to the anonymous referee for careful reading of the manuscript. This work was was supported in part by JSPS KAKENHI Grant Number JP17K05266.

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Authors and Affiliations

  1. Graduate School of Information Sciences, Tohoku University, Aoba-ku, Sendai, 980-8579, Japan

    Fumio Hiai

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  1. Fumio Hiai
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Correspondence to Fumio Hiai.

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Communicated by M. S. Moslehian.

Dedicated to Professor Rajendra Bhatia with admiration.

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Hiai, F. Operator means deformed by a fixed point method. Adv. Oper. Theory 5, 680–713 (2020). https://doi.org/10.1007/s43036-019-00034-9

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