{"title":"逐点James型常数","authors":"M. A. Rincón-Villamizar","doi":"10.1007/s10476-023-0221-7","DOIUrl":null,"url":null,"abstract":"<div><p>In 2008, Takahashi introduced the James type constants. We discuss here the pointwise James type constant: for all <i>x</i> ∈ <i>X</i>, ∥<i>x</i>∥ = 1, </p><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div><p> We show that in almost transitive Banach spaces, the map <i>x</i> ∈ <i>X</i>, ∥<i>x</i>∥ = 1 ↦ <i>J</i>(<i>x, X, t</i>) is constant. As a consequence and having in mind the Mazur’s rotation problem, we prove that for almost transitive Banach spaces, the condition <span>\\(J(x,X,t) = \\sqrt 2 \\)</span> for some unit vector <i>x</i> ∈ <i>X</i> implies that <i>X</i> is Hilbert.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The pointwise James type constant\",\"authors\":\"M. A. Rincón-Villamizar\",\"doi\":\"10.1007/s10476-023-0221-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In 2008, Takahashi introduced the James type constants. We discuss here the pointwise James type constant: for all <i>x</i> ∈ <i>X</i>, ∥<i>x</i>∥ = 1, </p><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div><p> We show that in almost transitive Banach spaces, the map <i>x</i> ∈ <i>X</i>, ∥<i>x</i>∥ = 1 ↦ <i>J</i>(<i>x, X, t</i>) is constant. As a consequence and having in mind the Mazur’s rotation problem, we prove that for almost transitive Banach spaces, the condition <span>\\\\(J(x,X,t) = \\\\sqrt 2 \\\\)</span> for some unit vector <i>x</i> ∈ <i>X</i> implies that <i>X</i> is Hilbert.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-06-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10476-023-0221-7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10476-023-0221-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In 2008, Takahashi introduced the James type constants. We discuss here the pointwise James type constant: for all x ∈ X, ∥x∥ = 1,
We show that in almost transitive Banach spaces, the map x ∈ X, ∥x∥ = 1 ↦ J(x, X, t) is constant. As a consequence and having in mind the Mazur’s rotation problem, we prove that for almost transitive Banach spaces, the condition \(J(x,X,t) = \sqrt 2 \) for some unit vector x ∈ X implies that X is Hilbert.
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