On a parametric family of distance measures that includes the Hellinger and the Bures distances

Article Mathematics

On Certain Order Properties of Non Kubo-Ando Means in Operator Algebras

Lajos Molnar

Summary: In this paper, we investigate important non Kubo-Ando means on the positive definite cones of C*-algebras and their relations to the usual (Lowner) order. We focus on whether these means satisfy the basic requirement and their monotonicity properties, and our results involve the central elements and commutativity of C*-algebras.

INTEGRAL EQUATIONS AND OPERATOR THEORY (2022)

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Article Mathematics, Applied

On dissimilarities of the conventional and Kubo-Ando power means in operator algebras *

Lajos Molnar

Summary: This paper investigates the differences between conventional power mean and Kubo-Ando power mean in operator algebras, including their fundamental properties and transformers. The study reveals significant dissimilarities between the two types of means, particularly in terms of their transformers.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2021)

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Article Mathematics, Applied

The α-z-Bures Wasserstein divergence

Trung Hoa Dinh et al.

Summary: This paper introduces a new matrix divergence for positive semidefinite matrices, which satisfies the Data Processing Inequality in quantum information. The least squares problem with respect to the new divergence is also solved, and the property of the matrix power mean with respect to the divergence is explored.

LINEAR ALGEBRA AND ITS APPLICATIONS (2021)

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Article Mathematics