{"title":"关于阶单元空间的几何","authors":"Anil Kumar Karn","doi":"10.1007/s43036-024-00327-8","DOIUrl":null,"url":null,"abstract":"<div><p>We introduce the notion of <i>skeleton</i> with a head in a non-zero real vector space. We prove that skeletons with a head describe order unit spaces geometrically. Next, we prove that the skeleton consists of boundary elements of the positive cone of norm one. We discuss some elementary properties of the skeleton. We also find a condition under which <i>V</i> contains a copy of <span>\\(\\ell _{\\infty }^n\\)</span> for some <span>\\(n \\in {\\mathbb {N}}\\)</span> as an order unit subspace.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the geometry of an order unit space\",\"authors\":\"Anil Kumar Karn\",\"doi\":\"10.1007/s43036-024-00327-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We introduce the notion of <i>skeleton</i> with a head in a non-zero real vector space. We prove that skeletons with a head describe order unit spaces geometrically. Next, we prove that the skeleton consists of boundary elements of the positive cone of norm one. We discuss some elementary properties of the skeleton. We also find a condition under which <i>V</i> contains a copy of <span>\\\\(\\\\ell _{\\\\infty }^n\\\\)</span> for some <span>\\\\(n \\\\in {\\\\mathbb {N}}\\\\)</span> as an order unit subspace.</p></div>\",\"PeriodicalId\":44371,\"journal\":{\"name\":\"Advances in Operator Theory\",\"volume\":\"9 2\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-03-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Operator Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43036-024-00327-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-024-00327-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We introduce the notion of skeleton with a head in a non-zero real vector space. We prove that skeletons with a head describe order unit spaces geometrically. Next, we prove that the skeleton consists of boundary elements of the positive cone of norm one. We discuss some elementary properties of the skeleton. We also find a condition under which V contains a copy of \(\ell _{\infty }^n\) for some \(n \in {\mathbb {N}}\) as an order unit subspace.
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