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math.RA2026
Invertible linear preservers of semipositive matrices - a dimension free approach
Vatsalkumar N. Mer
An m-by-n real matrix A is said to be semipositive if there exists a vector x>0 such that Ax>0, where the inequalities are understood componentwise. Dorsey et al. conjectured that…
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 $…