{"title":"整体函数的巴拿赫空间的评价函数和反身性","authors":"GUANGFU CAO, LI HE, JI LI, SHUQING ZHANG","doi":"10.1017/s1446788724000077","DOIUrl":null,"url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000077_inline1.png\"/> <jats:tex-math> $B(\\Omega )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> be a Banach space of holomorphic functions on a bounded connected domain <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000077_inline2.png\"/> <jats:tex-math> $\\Omega $ </jats:tex-math> </jats:alternatives> </jats:inline-formula> in <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000077_inline3.png\"/> <jats:tex-math> ${{\\mathbb C}^n}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. In this paper, we establish a criterion for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000077_inline4.png\"/> <jats:tex-math> $B(\\Omega )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> to be reflexive via evaluation functions on <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000077_inline5.png\"/> <jats:tex-math> $B(\\Omega )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, that is, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000077_inline6.png\"/> <jats:tex-math> $B(\\Omega )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is reflexive if and only if the evaluation functions span the dual space <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1446788724000077_inline7.png\"/> <jats:tex-math> $(B(\\Omega ))^{*} $ </jats:tex-math> </jats:alternatives> </jats:inline-formula>.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"EVALUATION FUNCTIONS AND REFLEXIVITY OF BANACH SPACES OF HOLOMORPHIC FUNCTIONS\",\"authors\":\"GUANGFU CAO, LI HE, JI LI, SHUQING ZHANG\",\"doi\":\"10.1017/s1446788724000077\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S1446788724000077_inline1.png\\\"/> <jats:tex-math> $B(\\\\Omega )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> be a Banach space of holomorphic functions on a bounded connected domain <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S1446788724000077_inline2.png\\\"/> <jats:tex-math> $\\\\Omega $ </jats:tex-math> </jats:alternatives> </jats:inline-formula> in <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S1446788724000077_inline3.png\\\"/> <jats:tex-math> ${{\\\\mathbb C}^n}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. In this paper, we establish a criterion for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S1446788724000077_inline4.png\\\"/> <jats:tex-math> $B(\\\\Omega )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> to be reflexive via evaluation functions on <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S1446788724000077_inline5.png\\\"/> <jats:tex-math> $B(\\\\Omega )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, that is, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S1446788724000077_inline6.png\\\"/> <jats:tex-math> $B(\\\\Omega )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> is reflexive if and only if the evaluation functions span the dual space <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S1446788724000077_inline7.png\\\"/> <jats:tex-math> $(B(\\\\Omega ))^{*} $ </jats:tex-math> </jats:alternatives> </jats:inline-formula>.\",\"PeriodicalId\":50007,\"journal\":{\"name\":\"Journal of the Australian Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-05-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Australian Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s1446788724000077\",\"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":"Journal of the Australian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s1446788724000077","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
EVALUATION FUNCTIONS AND REFLEXIVITY OF BANACH SPACES OF HOLOMORPHIC FUNCTIONS
Let $B(\Omega )$ be a Banach space of holomorphic functions on a bounded connected domain $\Omega $ in ${{\mathbb C}^n}$ . In this paper, we establish a criterion for $B(\Omega )$ to be reflexive via evaluation functions on $B(\Omega )$ , that is, $B(\Omega )$ is reflexive if and only if the evaluation functions span the dual space $(B(\Omega ))^{*} $ .
期刊介绍：
The Journal of the Australian Mathematical Society is the oldest journal of the Society, and is well established in its coverage of all areas of pure mathematics and mathematical statistics. It seeks to publish original high-quality articles of moderate length that will attract wide interest. Papers are carefully reviewed, and those with good introductions explaining the meaning and value of the results are preferred.
Published Bi-monthly
Published for the Australian Mathematical Society
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
