{"title":"全纯映射空间上的复合运算","authors":"María D Acosta;Pablo Galindo;Luiza A Moraes","doi":"10.1093/qmathj/haz035","DOIUrl":null,"url":null,"abstract":"We discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fréchet space of entire mappings that are bounded on bounded sets, the composition turns out to be even holomorphic. In such a space, we consider linear subspaces closed under left and right composition. We discuss the relationship of such subspaces with ideals of operators and give several examples of them. We also provide natural examples of spaces of holomorphic mappings where the composition is not continuous.","PeriodicalId":54522,"journal":{"name":"Quarterly Journal of Mathematics","volume":"71 1","pages":"557-572"},"PeriodicalIF":0.6000,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/qmathj/haz035","citationCount":"0","resultStr":"{\"title\":\"The Composition Operation on Spaces of Holomorphic Mappings\",\"authors\":\"María D Acosta;Pablo Galindo;Luiza A Moraes\",\"doi\":\"10.1093/qmathj/haz035\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fréchet space of entire mappings that are bounded on bounded sets, the composition turns out to be even holomorphic. In such a space, we consider linear subspaces closed under left and right composition. We discuss the relationship of such subspaces with ideals of operators and give several examples of them. We also provide natural examples of spaces of holomorphic mappings where the composition is not continuous.\",\"PeriodicalId\":54522,\"journal\":{\"name\":\"Quarterly Journal of Mathematics\",\"volume\":\"71 1\",\"pages\":\"557-572\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2020-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1093/qmathj/haz035\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Quarterly Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://ieeexplore.ieee.org/document/9266833/\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quarterly Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://ieeexplore.ieee.org/document/9266833/","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
The Composition Operation on Spaces of Holomorphic Mappings
We discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fréchet space of entire mappings that are bounded on bounded sets, the composition turns out to be even holomorphic. In such a space, we consider linear subspaces closed under left and right composition. We discuss the relationship of such subspaces with ideals of operators and give several examples of them. We also provide natural examples of spaces of holomorphic mappings where the composition is not continuous.
期刊介绍：
The Quarterly Journal of Mathematics publishes original contributions to pure mathematics. All major areas of pure mathematics are represented on the editorial board.
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