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arXiv · 2111.03256

Operator Spectral Geometric Versus Geometric Mean

Hamid Reza Moradi·Shigeru Furuichi·Mohammad Sababheh
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Abstract

The main goal of this article is to present new inequalities for the spectral geometric mean $A\natural_t B$ of two positive definite operators $A, B$ on a Hilbert space. The obtained results complement many known inequalities for the geometric mean $A\sharp_t B$. In particular, explicit comparisons between $A\natural_t B$ and $A\sharp_t B$ are given, with applications towards Ando-type inequalities and Ando-Hiai inequalities for $A\natural_t B$ and some other consequences.

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Hamid Reza Moradi, Shigeru Furuichi, Mohammad Sababheh. 2021-11-05. Operator Spectral Geometric Versus Geometric Mean. https://arxiv.org/abs/2111.03256

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