Derivations and homomorphisms in commutator-simple algebras
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909088579846144 |
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| author | Alaminos, J. Brešar, M. Extremera, J. Godoy, M. L. C. Villena, A. R. |
| author_facet | Alaminos, J. Brešar, M. Extremera, J. Godoy, M. L. C. Villena, A. R. |
| contents | We call an algebra $A$ commutator-simple if $[A,A]$ does not contain nonzero ideals of $A$. After providing several examples, we show that in these algebras derivations are determined by a condition that is applicable to the study of local derivations. This enables us to prove that every continuous local derivation $D\colon L^1(G)\to L^1(G)$, where $G$ is a unimodular locally compact group, is a derivation. We also give some remarks on homomorphism-like maps in commutator-simple algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_03460 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Derivations and homomorphisms in commutator-simple algebras Alaminos, J. Brešar, M. Extremera, J. Godoy, M. L. C. Villena, A. R. Functional Analysis 43A20, 47L10, 16W20, 16W25 We call an algebra $A$ commutator-simple if $[A,A]$ does not contain nonzero ideals of $A$. After providing several examples, we show that in these algebras derivations are determined by a condition that is applicable to the study of local derivations. This enables us to prove that every continuous local derivation $D\colon L^1(G)\to L^1(G)$, where $G$ is a unimodular locally compact group, is a derivation. We also give some remarks on homomorphism-like maps in commutator-simple algebras. |
| title | Derivations and homomorphisms in commutator-simple algebras |
| topic | Functional Analysis 43A20, 47L10, 16W20, 16W25 |
| url | https://arxiv.org/abs/2211.03460 |