{"title":"关于第一贝叶尔函数的某些类别","authors":"J. Mirmina, D. Puglisi","doi":"10.1007/s10474-024-01464-5","DOIUrl":null,"url":null,"abstract":"<div><p>We investigate first Baire functionals on the dual ball of a separable Banach space <span>\\(X\\)</span> which are pointwise limit of a sequence of <span>\\(X\\)</span> whose closed span does not contain any copy of <span>\\(\\ell_1\\)</span> (or has separable dual). We propose an example of a <span>\\(C(K)\\)</span> space where not all such first Baire functionals exhibit this behavior. \nAs an application, we study a quantitative version, in terms of descriptive set theory, of family a separable Banach spaces with this peculiarity. </p></div>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":"174 1","pages":"138 - 163"},"PeriodicalIF":0.6000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10474-024-01464-5.pdf","citationCount":"0","resultStr":"{\"title\":\"On certain classes of first Baire functionals\",\"authors\":\"J. Mirmina, D. Puglisi\",\"doi\":\"10.1007/s10474-024-01464-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We investigate first Baire functionals on the dual ball of a separable Banach space <span>\\\\(X\\\\)</span> which are pointwise limit of a sequence of <span>\\\\(X\\\\)</span> whose closed span does not contain any copy of <span>\\\\(\\\\ell_1\\\\)</span> (or has separable dual). We propose an example of a <span>\\\\(C(K)\\\\)</span> space where not all such first Baire functionals exhibit this behavior. \\nAs an application, we study a quantitative version, in terms of descriptive set theory, of family a separable Banach spaces with this peculiarity. </p></div>\",\"PeriodicalId\":50894,\"journal\":{\"name\":\"Acta Mathematica Hungarica\",\"volume\":\"174 1\",\"pages\":\"138 - 163\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10474-024-01464-5.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Acta Mathematica Hungarica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10474-024-01464-5\",\"RegionNum\":3,\"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":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10474-024-01464-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We investigate first Baire functionals on the dual ball of a separable Banach space \(X\) which are pointwise limit of a sequence of \(X\) whose closed span does not contain any copy of \(\ell_1\) (or has separable dual). We propose an example of a \(C(K)\) space where not all such first Baire functionals exhibit this behavior.
As an application, we study a quantitative version, in terms of descriptive set theory, of family a separable Banach spaces with this peculiarity.
期刊介绍：
Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.
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