An extension of the Kantorovich inequality to Hilbert spaces

Abstract

By using the singular value decomposition, we present an extension of the famous Kantorovich inequality for a class of operators on Hilbert spaces, including the invertible ones. In particular, this extends the Kantorovich inequality for positive definite matrices due to Greub and Rheinboldt. We also obtain a refinement of the finite-dimensional version of the Kantorovich inequality for invertible operators due to Strang.