Some Inequalities for Trace Class Operators Via a Kato's Result

TL;DR

This paper derives new inequalities for trace class operators on complex Hilbert spaces using Kato's inequality, with applications to functions of normal operators expressed by power series.

Contribution

It introduces novel trace inequalities based on Kato's inequality and applies them to functions of normal operators via power series expansions.

Findings

New trace inequalities for trace class operators.

Applications to functions of normal operators.

Enhanced bounds for operator functions.

Abstract

By the use of the celebrated Kato's inequality we obtain in this paper some new inequalities for trace class operators on a complex Hilbert space H. Natural applications for functions defined by power series of normal operators are given as well.