Name: An extension of the Kantorovich inequality to Hilbert spaces
Keywords: Inequalities in real analysis, Basic linear algebra, General theory of linear operators

descriptionPublicationkeyboard_double_arrow_right Article 05 Dec 2024Embargo end date: 01 Jan 2025Publisher:European Mathematical Society - EMS - Publishing House GmbHJournal:Elemente der Mathematik, volume 80, pages 78-83 (issn: 0013-6018, eissn: 1420-8962,

Authors: Saikat Roy; Debmalya Sain;

doi: 10.4171/em/541 , 10.5169/seals-1075494

An extension of the Kantorovich inequality to Hilbert spaces

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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.

Related Organizations

Tokyo University of Science
Japan
Indian Institute of Technology Hyderabad
India

Keywords

Inequalities in real analysis, Basic linear algebra, General theory of linear operators

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