Invertibility preserving mappings onto finite $C^*$-algebras
Volume 272 / 2023
Studia Mathematica 272 (2023), 113-120
MSC: Primary 47B48; Secondary 47A10, 46L05, 46L30, 16W10, 17C65.
DOI: 10.4064/sm230101-27-3
Published online: 29 May 2023
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.
