An extension of Kantorovich inequality to n-operators via the geometric mean by Ando–Li–Mathias

In this paper, we shall extend Kantorovich inequality. This is an estimate by using the geometric mean of n-operators which have been defined by Ando–Li–Mathias in [T. Ando, C. K. Li, R. Mathias, Geometric means, Linear Algebra Appl. 385 (2004) 305–334]. As a related result, we obtain a converse of arithmetic–geometric means inequality of n-operators via Kantorovich constant.