  It is well known that special Kubo-Ando operator means admit divergence
center interpretations, moreover, they are also mean squared error estimators
for certain metrics on positive definite operators. In this paper we give a
divergence center interpretation for every symmetric Kubo-Ando mean. This
characterization of the symmetric means naturally leads to a definition of
weighted and multivariate versions of a large class of symmetric Kubo-Ando
means. We study elementary properties of these weighted multivariate means, and
note in particular that in the special case of the geometric mean we recover
the weighted $\mathcal{A} \# \mathcal{H}$-mean introduced by Kim, Lawson, and
Lim.
