Jordan *-homomorphisms on the spaces of continuous maps taking values in C^*-algebras

2022/02/11 by Oi, Shiho
#46E40 #47B48 #47B49 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2202.05461

Abstract

Let A be a unital C^*-algebra. We consider Jordan *-homomorphisms on C(X, A) and Jordan *-homomorphisms on Lip(X,A). More precisely, for any unital C^*-algebra A, we prove that every Jordan *-homomorphism on C(X, A) and every Jordan *-homomorphism on Lip(X,A) is represented as a weighted composition operator by using the irreducible representations of A. In addition, when A₁ and A₂ are primitive C^*-algebras, we characterize the Jordan *-isomorphisms. These results unify and enrich previous works on algebra *-homomorphisms on C(X, A) and Lip(X,A) for several concrete examples of A.

Related

• Jordan *-homomorphisms between unital C^*-algebras
• Linear maps between C*-algebras that are *-homomorphisms at a fixed point
• Non-linear characterization of Jordan *-isomorphisms via maps on positive cones of C^*-algebras
• *-Jordan-type maps on C^*-algebras
• Invertibility preserving mappings onto finite C*-algebras