A note on Jensen inequality for self-adjoint operators

TL;DR

This paper explores a relation based on Jensen's inequality for self-adjoint operators in Hilbert spaces, demonstrating conditions under which this relation is antisymmetric.

Contribution

It introduces a new order-like relation for self-adjoint operators defined via Jensen inequality and proves its antisymmetry under certain assumptions.

Findings

The relation is antisymmetric under specific conditions.

Jensen inequality can define order-like relations for operators.

The paper provides theoretical insights into operator inequalities.

Abstract

In this paper we consider the order-like relation for self-adjoint operators on some Hilbert space. This relation is defined by using Jensen inequality. We will show that under some assumptions this relation is antisymmetric.