Operator means in JB-algebras

TL;DR

This paper introduces and studies operator means within JB-algebras, extending classical operator inequalities and identities from Hilbert space operators to this more general algebraic setting.

Contribution

It defines operator means in JB-algebras and establishes new identities and inequalities, adapting techniques from Hilbert space operators to JB-algebras.

Findings

Many classical operator inequalities are extended to JB-algebras.

New identities specific to JB-algebras are proved.

Techniques from Hilbert space operators are adapted for JB-algebras.

Abstract

In this paper, the notion of operator means in the setting of JB-algebras is introduced and their properties are studied. Many identities and inequalities are established, most of them have origins from operators on Hilbert space but they have different forms and connotations, and their proofs require techniques in JB-algebras.