Invertibility preserving mappings onto finite C*-algebras

TL;DR

This paper proves that any surjective unital linear map preserving invertibility from a Banach algebra onto a finite C*-algebra with a faithful trace is a Jordan homomorphism, extending previous results to a broader class of algebras.

Contribution

It generalizes Aupetit's 1998 result by establishing invertibility-preserving maps as Jordan homomorphisms for finite C*-algebras with a faithful tracial state.

Findings

Surjective unital invertibility-preserving maps are Jordan homomorphisms.

Extension of Aupetit's 1998 result to finite C*-algebras with faithful traces.

Broader class of algebras where invertibility-preserving maps are characterized.

Abstract

We prove that every surjective unital linear mapping which preserves invertible elements from a Banach algebra onto a C*-algebra carrying a faithful tracial state is a Jordan homomorphism thus generalising Aupetit's 1998 result for finite von Neumann algebras.