{"title":"可服从拟格序群与真表示","authors":"M-Alamin A. H. Ahmed","doi":"10.5269/bspm.62552","DOIUrl":null,"url":null,"abstract":"Let (G, P) be a quasi-lattice ordered group. In [2] we constructed a universal covariant representation (A,U) for (G, P) in a way that avoids some of the intricacies of the other approaches in [11] and [8]. Then we showed if (G, P) is amenable, true representations of (G, P) generate C∗-algebras which are canonically isomorphic to the C∗-algebra generated by the universal covariant representation. In this paper, we discuss characterizations of amenability in a comparatively simple and natural way to introduce this formidable property. Amenability of (G, P) can be established by investigating the behavior of ΦU on the range of a positive, faithful, linear map rather than the whole algebra.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2022-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Amenable quase-lattice ordered groups and true representations\",\"authors\":\"M-Alamin A. H. Ahmed\",\"doi\":\"10.5269/bspm.62552\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let (G, P) be a quasi-lattice ordered group. In [2] we constructed a universal covariant representation (A,U) for (G, P) in a way that avoids some of the intricacies of the other approaches in [11] and [8]. Then we showed if (G, P) is amenable, true representations of (G, P) generate C∗-algebras which are canonically isomorphic to the C∗-algebra generated by the universal covariant representation. In this paper, we discuss characterizations of amenability in a comparatively simple and natural way to introduce this formidable property. Amenability of (G, P) can be established by investigating the behavior of ΦU on the range of a positive, faithful, linear map rather than the whole algebra.\",\"PeriodicalId\":44941,\"journal\":{\"name\":\"Boletim Sociedade Paranaense de Matematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-12-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Boletim Sociedade Paranaense de Matematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5269/bspm.62552\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Boletim Sociedade Paranaense de Matematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5269/bspm.62552","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Amenable quase-lattice ordered groups and true representations
Let (G, P) be a quasi-lattice ordered group. In [2] we constructed a universal covariant representation (A,U) for (G, P) in a way that avoids some of the intricacies of the other approaches in [11] and [8]. Then we showed if (G, P) is amenable, true representations of (G, P) generate C∗-algebras which are canonically isomorphic to the C∗-algebra generated by the universal covariant representation. In this paper, we discuss characterizations of amenability in a comparatively simple and natural way to introduce this formidable property. Amenability of (G, P) can be established by investigating the behavior of ΦU on the range of a positive, faithful, linear map rather than the whole algebra.