The ALM-Framework in the Theory of Multivariate Operator Means

In this paper, we generalize the ALM-procedure introduced by Ando, Li, and Mathias for extending operator geometric means to multiple variables. We prove that the generalized procedure preserves all the properties required by the axioms of operator means, along with several additional desirable properties. Moreover, we examine the self-adjointness of the canonical geometric mean constructed through this procedure.