C^\ast $-代数上的映射是一点上的斜李三重导数或同态

IF 1.8 3区数学 Q1 MATHEMATICS

AIMS Mathematics Pub Date : 2023-01-01 DOI:10.3934/math.20231305

Zhonghua Wang, Xiuhai Fei

{"title":"C^\\ast $-代数上的映射是一点上的斜李三重导数或同态","authors":"Zhonghua Wang, Xiuhai Fei","doi":"10.3934/math.20231305","DOIUrl":null,"url":null,"abstract":"In this paper, we show that every continuous linear map between unital $ C^\\ast $-algebras is skew Lie triple derivable at the identity is a $ \\ast $-derivation and that every continuous linear map between unital $ C^\\ast $-algebras which is a skew Lie triple homomorphism at the identity is a Jordan $ \\ast $-homomorphism.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Maps on $ C^\\\\ast $-algebras are skew Lie triple derivations or homomorphisms at one point\",\"authors\":\"Zhonghua Wang, Xiuhai Fei\",\"doi\":\"10.3934/math.20231305\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we show that every continuous linear map between unital $ C^\\\\ast $-algebras is skew Lie triple derivable at the identity is a $ \\\\ast $-derivation and that every continuous linear map between unital $ C^\\\\ast $-algebras which is a skew Lie triple homomorphism at the identity is a Jordan $ \\\\ast $-homomorphism.\",\"PeriodicalId\":48562,\"journal\":{\"name\":\"AIMS Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"AIMS Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3934/math.20231305\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"AIMS Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3934/math.20231305","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文证明了一元C^\ast $-代数之间的每一个连续线性映射在单位上都是偏李三重可导的，是一元C^\ast $-导数;一元C^\ast $-代数之间的每一个连续线性映射在单位上都是偏李三重同态的，是Jordan $ \ast $-同态。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Maps on $ C^\ast $-algebras are skew Lie triple derivations or homomorphisms at one point

In this paper, we show that every continuous linear map between unital $ C^\ast $-algebras is skew Lie triple derivable at the identity is a $ \ast $-derivation and that every continuous linear map between unital $ C^\ast $-algebras which is a skew Lie triple homomorphism at the identity is a Jordan $ \ast $-homomorphism.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

AIMS Mathematics Mathematics-General Mathematics

CiteScore

3.40

自引率

13.60%

发文量

769

审稿时长

90 days

期刊介绍： AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.