An asymmetric Kadison's inequality

TL;DR

This paper introduces asymmetric extensions of Kadison's inequality and explores operator versions of Chebyshev's inequality, connecting matrix geometric mean with complex interpolation to advance understanding of inequalities in matrix algebras.

Contribution

It provides novel asymmetric inequalities for positive linear maps and links matrix geometric mean with complex interpolation, expanding the theoretical framework of operator inequalities.

Findings

New asymmetric Kadison's inequalities for positive linear maps

Operator versions of Chebyshev's inequality derived

Connections established between matrix geometric mean and complex interpolation

Abstract

Some inequalities for positive linear maps on matrix algebras are given, especially asymmetric extensions of Kadison's inequality and several operator versions of Chebyshev's inequality. We also discuss well-known results around the matrix geometric mean and connect it with complex interpolation.