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math.FA2026
On the Wasserstein barycenter of positive definite operators
Sejong Kim, Vatsalkumar N. Mer, Miklós Pálfia
We extend the Bures-Wasserstein mean of positive definite matrices to the case of positive definite operators on a Hilbert space. This is done through its defining stationary point…
math.FA2026
A multivariable mean equation arising from the spectral geometric mean
Sejong Kim, Vatsalkumar N. Mer
In the 1980s, Kubo and Ando introduced operator means on , the open convex cone of positive definite operators. One significant example is the weighted geometric mean $…
math.FA2024
New multivariable mean from nonlinear matrix equation associated to the harmonic mean
Sejong Kim, Vatsalkumar N. Mer
Various multivariable means have been defined for positive definite matrices, such as the Cartan mean, Wasserstein mean, and Rényi power mean. These multivariable means have corres…