Reverses of Ando's and H\"older-Macarty's inequalities

TL;DR

This paper develops reverse inequalities related to Ando's and H"older-McCarthy's inequalities for positive linear maps and invertible operators, utilizing recent improvements in Young's inequality.

Contribution

It introduces new reverse inequalities for classical operator inequalities using an improved Young inequality framework.

Findings

Established reverse inequalities for Ando's and H"older-McCarthy's inequalities.

Extended the inequalities to positive invertible operators.

Utilized a recently improved Young inequality and its reverse.

Abstract

In this paper, we give some reverse-types of Ando's and H\"older-McCarthy's inequalities for positive linear maps, and positive invertible operators. For our purpose, we use a recently improved Young inequality and its reverse.