Improved Young and Heinz inequalities with the Kantorovich constant

TL;DR

This paper presents new refinements and reverses of Young and Heinz inequalities using the Kantorovich constant, leading to improved operator and Hilbert-Schmidt norm inequalities on Hilbert spaces.

Contribution

The paper introduces novel refinements and reverses of classical inequalities with the Kantorovich constant, extending their applicability to operator and Hilbert-Schmidt norm inequalities.

Findings

Refined Young and Heinz inequalities with Kantorovich constant

Operator inequalities on Hilbert space established

Hilbert-Schmidt norm inequalities derived

Abstract

In this article, we study the further refinements and reverses of the Young and Heinz inequalities with the Kantorovich constant. These modified inequalities are used to establish corresponding operator inequalities on Hilbert space and Hilbert-Schmidt norm inequalities.