On a new construction of geometric mean of \(n\)-operators
\textit{W.\,Pusz} and \textit{S.\,L.\thinspace Woronowicz} [Rep.\ Math.\ Phys.\ 8, 159--170 (1975; Zbl 0327.46032)] introduced the geometric mean of two positive invertible operators \(A\) and \(B\) as \[ A \sharp B = A^{1/2}(A^{-1/2}BA^{-1/2})^{1/2}A^{1/2}. \] One cannot immediately use this definition for defining the geometric mean of \(n\) operators. \textit{T.\,Ando}, \textit{C.\,K.\thinspace Li} and \textit{R.\,Mathias} [Linear Algebra Appl.\ 385, 305--334 (2004; Zbl 1063.47013)] defined the geometric mean of \(n\) positive definite operators by a symmetric procedure. Their definition requires an enormous amount of calculation. In the paper under review, the authors introduce a new construction of the geometric mean of \(n\) operators, which can be obtained easier than the geometric mean of Ando--Li--Mathias.
scientific article; zbMATH DE number 5603566
scientific article