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arXiv · 2608.04344

Kubo Ando Means on the Cone of J Hermitian Matrices

Sebastian Micalizzi·Hayden Tyler
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Abstract

The theory of Kubo-Ando means provides a fundamental correspondence between operator means and operator monotone functions on the positive half-line. In this paper, we first extend this theory to the cone of positive quaternionic Hermitian matrices, establishing quaternionic analogues of the main results of Kubo and Ando. We then develop an analogous framework for the cone of J-Hermitian positive matrices associated with an indefinite inner product. In particular, we prove that Kubo-Ando means on this cone are again in one-to-one correspondence with operator monotone functions, thereby extending the classical characterization to this indefinite setting.

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Sebastian Micalizzi, Hayden Tyler. 2026-08-05. Kubo Ando Means on the Cone of J Hermitian Matrices. https://arxiv.org/abs/2608.04344

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