On a new construction of geometric mean of n-operators

For n positive definite operators A1,…,An, Ando-Li-Mathias defined geometric mean of n-operators G(A1,…,An) 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.