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arXiv · 1810.05476

Matrix limit theorems of Kato type related to positive linear maps and operator means

Fumio Hiai
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Abstract

We obtain limit theorems for $Φ(A^p)^{1/p}$ and $(A^pσB)^{1/p}$ as $p\to\infty$ for positive matrices $A,B$, where $Φ$ is a positive linear map between matrix algebras (in particular, $Φ(A)=KAK^*$) and $σ$ is an operator mean (in particular, the weighted geometric mean), which are considered as certain reciprocal Lie-Trotter formulas and also a generalization of Kato's limit to the supremum $A\vee B$ with respect to the spectral order.

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Fumio Hiai. 2018-10-12. Matrix limit theorems of Kato type related to positive linear maps and operator means. https://arxiv.org/abs/1810.05476

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