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Log-majorizations between quasi-geometric type means for matrices

arXiv

Authors: Fumio Hiai

Year

2025

Paper ID

51807

Status

Preprint

Abstract Read

~2 min

Abstract Words

106

Citations

N/A

Abstract

In this paper, for αin\(0,infty\)setminus\{1\}, p>0 and positive semidefinite matrices A and B, we consider the quasi-extension mathcal{M}_α,p(A,B):=mathcal{M}_α\(A^p,B^p\)^1/p of several α-weighted geometric type matrix means mathcal{M}_α(A,B) such as the α-weighted geometric mean in Kubo--Ando's sense, the Rényi mean, etc. The log-majorization mathcal{M}_α,p(A,B)prec_logmathcal{N}_α,q(A,B) is examined for pairs \(mathcal{M},mathcal{N}\) of those α-weighted geometric type means. The joint concavity/convexity of the trace functions Tr mathcal{M}_α,p is also discussed based on theory of quantum divergences.

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In this paper, for αin(0,infty)setminus1, p>0 and positive semidefinite matrices A and B, we consider the quasi-extension mathcalMα,p(A,B):=mathcalM_α(A^p,B^p^1/p) of several...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2510.04691 [2] arXiv https://arxiv.org/abs/2510.04691 [3] Publisher https://arxiv.org/abs/2510.04691

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