Weighted geometric mean of \(n\)-operators with \(n\)-parameters (Q846304)

Based on the geometric mean defined by \textit{C.\,D.\thinspace Jung}, \textit{H.\,S.\thinspace Lee} and \textit{T.\,Yamazaki} [Linear Algebra Appl.\ 431, No.\,9, 1477--1488 (2009; Zbl 1172.47017)], the authors introduce a weighted geometric mean of \(n\) operators with \(n\) parameters. It needs \(n\) parameters for weights at the outset, but does not require enormous calculations to get a concrete form. The final weights can be described by a simple form if the \(n\)-tuple of operators is commutative.