Theoretical Statistics and Mathematics Unit, ISI Delhi

Mean matrices and infinite divisibility

by Rajendra Bhatia and Hideki Kosaki

We consider matrices $M$ with entries $m_{ij} = m (\lambda_i, \lambda_j)$
where $\lambda_1, \ldots, \lambda_n$ are positive numbers and $m$ is a binary mean dominated
by the geometric mean, and matrices $W$ with entries $w_{ij} = 1/m (\lambda_i, \lambda_j)$
where $m$ is a binary mean that dominates the geometric mean.
We show that these matrices are infinitely divisible for several much-studied classes of means.

isid/ms/2006/05 [fulltext]

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