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arXiv · 2512.22807

On the Ando-Hiai property for spectral geometric means

Yuki Seo·Shuhei Wada·Takeaki Yamazaki
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Abstract

In this paper, we consider a two-variable operator function that includes two weighted spectral geometric means, and show fundamental properties of the operator function. Moreover, it satisfies the Ando-Hiai type inequality under some restricted conditions. As an application, we show the log-majorization relations and norm inequalities for the spectral geometric means of positive definite matrices.

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Yuki Seo, Shuhei Wada, Takeaki Yamazaki. 2025-12-28. On the Ando-Hiai property for spectral geometric means. https://arxiv.org/abs/2512.22807

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