{"title":"Enveloping Dual Banach Algebras and Approximate Properties","authors":"N. Razi, A. Pourabbas","doi":"10.1155/2024/6300080","DOIUrl":null,"url":null,"abstract":"Suppose that <svg height=\"8.68572pt\" style=\"vertical-align:-0.0498209pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 9.2729 8.68572\" width=\"9.2729pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg> is a Banach algebra and <svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 26.2232 11.5564\" width=\"26.2232pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,7.895,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,12.393,0)\"><use xlink:href=\"#g113-66\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.528,0)\"></path></g></svg> is its enveloping dual Banach algebra, we show that <svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 26.2232 11.5564\" width=\"26.2232pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-71\"></use></g><g transform=\"matrix(.013,0,0,-0.013,7.895,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,12.393,0)\"><use xlink:href=\"#g113-66\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.528,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> is approximately contractible (approximately amenable) if <svg height=\"8.68572pt\" style=\"vertical-align:-0.0498209pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 9.2729 8.68572\" width=\"9.2729pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-66\"></use></g></svg> has the same property. Also, we study the relation between the pseudoamenability of <svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 26.2232 11.5564\" width=\"26.2232pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-71\"></use></g><g transform=\"matrix(.013,0,0,-0.013,7.895,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,12.393,0)\"><use xlink:href=\"#g113-66\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.528,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> and the pseudoamenability of the second dual <svg height=\"10.1524pt\" style=\"vertical-align:-0.04990005pt\" version=\"1.1\" viewbox=\"-0.0498162 -10.1025 20.9329 10.1524\" width=\"20.9329pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-66\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,9.135,-5.741)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,14.695,-5.741)\"><use xlink:href=\"#g50-43\"></use></g></svg> and we also characterize approximate biflatness and approximate biprojectivity of <svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 26.2232 11.5564\" width=\"26.2232pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-71\"></use></g><g transform=\"matrix(.013,0,0,-0.013,7.895,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,12.393,0)\"><use xlink:href=\"#g113-66\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.528,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> associated with approximate biflatness and approximate biprojectivity of the second dual <span><svg height=\"10.1524pt\" style=\"vertical-align:-0.04990005pt\" version=\"1.1\" viewbox=\"-0.0498162 -10.1025 20.9329 10.1524\" width=\"20.9329pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-66\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,9.135,-5.741)\"><use xlink:href=\"#g50-43\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,14.695,-5.741)\"><use xlink:href=\"#g50-43\"></use></g></svg>.</span>","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"16 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1155/2024/6300080","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Suppose that is a Banach algebra and is its enveloping dual Banach algebra, we show that is approximately contractible (approximately amenable) if has the same property. Also, we study the relation between the pseudoamenability of and the pseudoamenability of the second dual and we also characterize approximate biflatness and approximate biprojectivity of associated with approximate biflatness and approximate biprojectivity of the second dual .
期刊介绍：
Journal of Mathematics is a broad scope journal that publishes original research articles as well as review articles on all aspects of both pure and applied mathematics. As well as original research, Journal of Mathematics also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.
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