Jordan Left α-centralizers on Algebras with Applications to Group Algebras

2025/08/04 by M. Eisaei, Eisaei, M., M. J. Mehdipour +3
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results

paper · pdf · doi:10.48550/arxiv.2508.02114

openalex publication_date 2025/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every Jordan left α-centralizer from an algebra A with a right identity into an arbitrary algebra B is a left α-centralizer. This implies all Jordan homomorphisms between such algebras are homomorphisms. We extend this result to continuous Jordan left α-centralizers when A has a bounded left approximate identity. For the group algebra L¹(G), we characterize weakly compact Jordan left α-centralizers when α is continuous and surjective, showing L¹(G) admits a weakly compact epimorphism if and only if G is finite. Consequently, the existence of a non-zero α-derivation on L¹(G) is equivalent to G being compact and non-abelian.

Citations

• Regularity and amenability of weighted Banach algebras and their second dual on locally compact groups

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