{"title":"对偶巴拿赫代数的双突变定理","authors":"Matthew Daws","doi":"10.3318/PRIA.2011.111.1.3","DOIUrl":null,"url":null,"abstract":"A dual Banach algebra is a Banach algebra which is a dual space, with the multiplication being separately weak$^*$-continuous. We show that given a unital dual Banach algebra $\\mc A$, we can find a reflexive Banach space $E$, and an isometric, weak$^*$-weak$^*$-continuous homomorphism $\\pi:\\mc A\\to\\mc B(E)$ such that $\\pi(\\mc A)$ equals its own bicommutant.","PeriodicalId":434988,"journal":{"name":"Mathematical Proceedings of the Royal Irish Academy","volume":"36 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"A BICOMMUTANT THEOREM FOR DUAL BANACH ALGEBRAS\",\"authors\":\"Matthew Daws\",\"doi\":\"10.3318/PRIA.2011.111.1.3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A dual Banach algebra is a Banach algebra which is a dual space, with the multiplication being separately weak$^*$-continuous. We show that given a unital dual Banach algebra $\\\\mc A$, we can find a reflexive Banach space $E$, and an isometric, weak$^*$-weak$^*$-continuous homomorphism $\\\\pi:\\\\mc A\\\\to\\\\mc B(E)$ such that $\\\\pi(\\\\mc A)$ equals its own bicommutant.\",\"PeriodicalId\":434988,\"journal\":{\"name\":\"Mathematical Proceedings of the Royal Irish Academy\",\"volume\":\"36 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-01-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Proceedings of the Royal Irish Academy\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3318/PRIA.2011.111.1.3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Proceedings of the Royal Irish Academy","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3318/PRIA.2011.111.1.3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
摘要
对偶巴拿赫代数是一个巴拿赫代数，它是一个对偶空间，其乘法分别是弱$^*$连续的。我们证明了给定一个一元对偶巴拿赫代数$\mc a $，我们可以找到一个自反巴拿赫空间$E$，以及一个等距的弱$^*$-弱$^*$-连续同态$\pi:\mc a $到\mc B(E)$使得$\pi(\mc a)$等于它自己的双元突变体$。
A dual Banach algebra is a Banach algebra which is a dual space, with the multiplication being separately weak$^*$-continuous. We show that given a unital dual Banach algebra $\mc A$, we can find a reflexive Banach space $E$, and an isometric, weak$^*$-weak$^*$-continuous homomorphism $\pi:\mc A\to\mc B(E)$ such that $\pi(\mc A)$ equals its own bicommutant.
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