{"title":"三个巴拿赫代数的乘积","authors":"A. Khotanloo","doi":"10.29252/MACO.1.2.2","DOIUrl":null,"url":null,"abstract":". Let A , B , and C be Banach algebras, (cid:11) 2 Hom ( A ; B ) and (cid:12) 2 Hom ( C ; B ) , and ∥ (cid:11) ∥(cid:20) 1 , ∥ (cid:12) ∥(cid:20) 1 . IN this paper we define the Banach algebra A(cid:2) (cid:11) B(cid:2) (cid:12) C by new product on A(cid:2)B(cid:2)C which is a strongly splitting extension of C by B . Then we show that these products from a large class of Banach algebras which contains all module extensions and triangular Banach algebras. Finally we consider spectrum, Arens regularity, amenability and weak amenability of these products.","PeriodicalId":360771,"journal":{"name":"Mathematical Analysis and Convex Optimization","volume":"417 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Product Between Three Banach Algebras\",\"authors\":\"A. Khotanloo\",\"doi\":\"10.29252/MACO.1.2.2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". Let A , B , and C be Banach algebras, (cid:11) 2 Hom ( A ; B ) and (cid:12) 2 Hom ( C ; B ) , and ∥ (cid:11) ∥(cid:20) 1 , ∥ (cid:12) ∥(cid:20) 1 . IN this paper we define the Banach algebra A(cid:2) (cid:11) B(cid:2) (cid:12) C by new product on A(cid:2)B(cid:2)C which is a strongly splitting extension of C by B . Then we show that these products from a large class of Banach algebras which contains all module extensions and triangular Banach algebras. Finally we consider spectrum, Arens regularity, amenability and weak amenability of these products.\",\"PeriodicalId\":360771,\"journal\":{\"name\":\"Mathematical Analysis and Convex Optimization\",\"volume\":\"417 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Analysis and Convex Optimization\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.29252/MACO.1.2.2\",\"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 Analysis and Convex Optimization","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.29252/MACO.1.2.2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
. Let A , B , and C be Banach algebras, (cid:11) 2 Hom ( A ; B ) and (cid:12) 2 Hom ( C ; B ) , and ∥ (cid:11) ∥(cid:20) 1 , ∥ (cid:12) ∥(cid:20) 1 . IN this paper we define the Banach algebra A(cid:2) (cid:11) B(cid:2) (cid:12) C by new product on A(cid:2)B(cid:2)C which is a strongly splitting extension of C by B . Then we show that these products from a large class of Banach algebras which contains all module extensions and triangular Banach algebras. Finally we consider spectrum, Arens regularity, amenability and weak amenability of these products.
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