Additivity of maps preserving Jordan η_∗-products on C^*-algebras

2015/04/01 by Ali Taghavi, Taghavi, Ali, Hamid Rohi +3
Mathematics · #46L10 #47B48 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Equations Stability Results #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1504.00100

openalex publication_date 2015/04/01 · openalex created_date 2022/08/31 · openalex updated_date 2026/07/28

Abstract

Let A and B be two C^*-algebras such that B is prime. In this paper, we investigate the additivity of map Φ from A onto B that are bijective unital and satisfies Φ(AP+ηPA^*)=Φ(A)Φ(P)+ηΦ(P)Φ(A)^*, for all A\inA and P∈\P₁,I_A-P₁\ where P₁ is a nontrivial projection in A. Let η be a non-zero complex number such that |η|≠1, then Φ is additive. Moreover, if η is rational then Φ is ∗-additive.

Related

• Additivity of maps preserving products AP± PA^* on C^*-algebras
• Mappings preserving sum of triple products on ∗ -algebras
• *-Jordan-type maps on C^*-algebras
• Nonlinear maps preserving sums of triple products on ∗ -algebras
• Nonlinear maps preserving Jordan η-∗-n-products