On a new construction of geometric mean of n-operators

Abstract For n positive definite operators A 1 , … , A n , Ando-Li-Mathias defined geometric mean of n -operators G ( A 1 , … , A n ) by symmetric procedure. It has many nice properties, and is studied by many authors. But the process is so complicated to compute. In this paper, we shall attempt to make a new construction of geometric mean of n -operators which we can compute it easier than geometric mean by Ando–Li–Mathias.