Weighted Lim’s Geometric Mean of Positive Invertible Operators on a Hilbert Space

Authors

Keywords:

positive invertible operator, metric geometric mean, spectral geometric mean, Lim’s geometric mean, Tracy-Singh product

Abstract

We generalize the weighted Lim’s geometric mean of positive definite matrices to positive invertible operators on a Hilbert space. This mean is defined via a certain bijection map and parametrized over Hermitian unitary operators. We derive an explicit formula of the weighted Lim’s geometric mean in terms of weighted metric/spectral geometric means. This kind of operator mean turns out to be a symmetric Lim-P´alfia weighted mean and satisfies the idempotency, the permutation invariance, the joint homogeneity, the self-duality, and the unitary invariance. Moreover, we obtain relations between weighted Lim geometric means and Tracy-Singh products via operator identities

Downloads

Published

2021-03-13

How to Cite

Arnon Ploymukda, & Pattrawut Chansangiam. (2021). Weighted Lim’s Geometric Mean of Positive Invertible Operators on a Hilbert Space. Journal of Computational Analysis and Applications (JoCAAA), 29(2), 390–400. Retrieved from https://eudoxuspress.com/index.php/pub/article/view/158

Issue

Section

Articles

Similar Articles

<< < 15 16 17 18 19 20 

You may also start an advanced similarity search for this article.