{"title":"纯⁎同构","authors":"Joan Bosa , Eduard Vilalta","doi":"10.1016/j.jfa.2024.110739","DOIUrl":null,"url":null,"abstract":"<div><div>We introduce and study the notion of pureness for *-homomorphisms and, more generally, for cpc order-zero maps. After providing various important examples of pureness, we show our main result: Any composition of two pure maps factors through a pure object up to Cuntz equivalence. This is used to obtain several factorization results at the level of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebras.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"288 3","pages":"Article 110739"},"PeriodicalIF":1.7000,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Pure ⁎-homomorphisms\",\"authors\":\"Joan Bosa , Eduard Vilalta\",\"doi\":\"10.1016/j.jfa.2024.110739\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We introduce and study the notion of pureness for *-homomorphisms and, more generally, for cpc order-zero maps. After providing various important examples of pureness, we show our main result: Any composition of two pure maps factors through a pure object up to Cuntz equivalence. This is used to obtain several factorization results at the level of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebras.</div></div>\",\"PeriodicalId\":15750,\"journal\":{\"name\":\"Journal of Functional Analysis\",\"volume\":\"288 3\",\"pages\":\"Article 110739\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-11-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Functional Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022123624004270\",\"RegionNum\":2,\"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":"Journal of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022123624004270","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
We introduce and study the notion of pureness for *-homomorphisms and, more generally, for cpc order-zero maps. After providing various important examples of pureness, we show our main result: Any composition of two pure maps factors through a pure object up to Cuntz equivalence. This is used to obtain several factorization results at the level of -algebras.
期刊介绍：
The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published.
Research Areas Include:
• Significant applications of functional analysis, including those to other areas of mathematics
• New developments in functional analysis
• Contributions to important problems in and challenges to functional analysis
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