Jordan Left $α$-centralizers on Algebras with Applications to Group Algebras
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911090223349760 |
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| author | Eisaei, M. Mehdipour, M. J. Moghimi, Gh. R. |
| author_facet | Eisaei, M. Mehdipour, M. J. Moghimi, Gh. R. |
| contents | 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 $L^1(G)$, we characterize weakly compact Jordan left $α$-centralizers when $α$ is continuous and surjective, showing $L^1(G)$ admits a weakly compact epimorphism if and only if $G$ is finite. Consequently, the existence of a non-zero $α$-derivation on $L^1(G)$ is equivalent to $G$ being compact and non-abelian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_02114 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Jordan Left $α$-centralizers on Algebras with Applications to Group Algebras Eisaei, M. Mehdipour, M. J. Moghimi, Gh. R. Functional Analysis 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 $L^1(G)$, we characterize weakly compact Jordan left $α$-centralizers when $α$ is continuous and surjective, showing $L^1(G)$ admits a weakly compact epimorphism if and only if $G$ is finite. Consequently, the existence of a non-zero $α$-derivation on $L^1(G)$ is equivalent to $G$ being compact and non-abelian. |
| title | Jordan Left $α$-centralizers on Algebras with Applications to Group Algebras |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2508.02114 |