Nearly Jordan -Homomorphisms between Unital -Algebras

Abstract

Let A , B be two unital C ∗ ‐algebras. We prove that every almost unital almost linear mapping h : A → B which satisfies h (3 n u y + 3 n y u ) = h (3 n u ) h ( y ) + h ( y ) h (3 n u ) for all u ∈ U ( A ), all y ∈ A , and all n = 0,1, 2, …, is a Jordan homomorphism. Also, for a unital C ∗ ‐algebra A of real rank zero, every almost unital almost linear continuous mapping h : A → B is a Jordan homomorphism when h (3 n u y + 3 n y u ) = h (3 n u ) h ( y ) + h ( y ) h (3 n u ) holds for all u ∈ I 1 ( A sa ), all y ∈ A , and all n = 0,1, 2, …. Furthermore, we investigate the Hyers‐ Ulam‐Aoki‐Rassias stability of Jordan ∗‐homomorphisms between unital C ∗ ‐algebras by using the fixed points methods.

Locations

• Project Euclid (Cornell University) - View - PDF
• DOAJ (DOAJ: Directory of Open Access Journals) - View
• Abstract and Applied Analysis - View - PDF