与巴拿赫空间中的伯克霍夫正交性有关的邓克尔-威廉斯常数

IF 0.7 4区数学 Q2 MATHEMATICS

Bulletin of The Iranian Mathematical Society Pub Date : 2024-02-26 DOI:10.1007/s41980-023-00853-w

Yuankang Fu, Huayou Xie, Yongjin Li

{"title":"与巴拿赫空间中的伯克霍夫正交性有关的邓克尔-威廉斯常数","authors":"Yuankang Fu, Huayou Xie, Yongjin Li","doi":"10.1007/s41980-023-00853-w","DOIUrl":null,"url":null,"abstract":"In this paper, we shall consider a new constant \\(DW_B(X)\\) which is the Dunkl–Williams constant related to Birkhoff orthogonality, and a constant \\(DW^p_B(X)\\) that is a generalization of \\(DW_B(X)\\). Interestingly, the upper bounds of \\(DW_B(X)\\) and the Dunkl–Williams constant are different. The connections between these two constants and other well-known constants are exhibited. Some characterizations of Hilbert space and uniformly non-square Banach space in terms of these two constants are established. Furthermore, we also give a characterization of the Radon plane with an affine regular hexagonal unit sphere and calculate the value of \\(DW^p_B(l_\\infty -l_1)\\).","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Dunkl–Williams Constant Related to Birkhoff Orthogonality in Banach Spaces\",\"authors\":\"Yuankang Fu, Huayou Xie, Yongjin Li\",\"doi\":\"10.1007/s41980-023-00853-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we shall consider a new constant \\\\(DW_B(X)\\\\) which is the Dunkl–Williams constant related to Birkhoff orthogonality, and a constant \\\\(DW^p_B(X)\\\\) that is a generalization of \\\\(DW_B(X)\\\\). Interestingly, the upper bounds of \\\\(DW_B(X)\\\\) and the Dunkl–Williams constant are different. The connections between these two constants and other well-known constants are exhibited. Some characterizations of Hilbert space and uniformly non-square Banach space in terms of these two constants are established. Furthermore, we also give a characterization of the Radon plane with an affine regular hexagonal unit sphere and calculate the value of \\\\(DW^p_B(l_\\\\infty -l_1)\\\\).\",\"PeriodicalId\":9395,\"journal\":{\"name\":\"Bulletin of The Iranian Mathematical Society\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-02-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of The Iranian Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s41980-023-00853-w\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Iranian Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s41980-023-00853-w","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

在本文中，我们将考虑一个新的常数 \(DW_B(X)\)，它是与伯克霍夫正交性相关的邓克尔-威廉常数，以及一个常数 \(DW^p_B(X)\)，它是\(DW_B(X)\)的广义化。有趣的是，\(DW_B(X)\)和邓克尔-威廉常数的上限是不同的。本文展示了这两个常数与其他著名常数之间的联系。用这两个常数建立了希尔伯特空间和均匀非平方巴拿赫空间的一些特征。此外，我们还给出了具有仿射正六边形单位球的拉顿平面的特征，并计算了 \(DW^p_B(l_\infty-l_1)\)的值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

The Dunkl–Williams Constant Related to Birkhoff Orthogonality in Banach Spaces

In this paper, we shall consider a new constant \(DW_B(X)\) which is the Dunkl–Williams constant related to Birkhoff orthogonality, and a constant \(DW^p_B(X)\) that is a generalization of \(DW_B(X)\). Interestingly, the upper bounds of \(DW_B(X)\) and the Dunkl–Williams constant are different. The connections between these two constants and other well-known constants are exhibited. Some characterizations of Hilbert space and uniformly non-square Banach space in terms of these two constants are established. Furthermore, we also give a characterization of the Radon plane with an affine regular hexagonal unit sphere and calculate the value of \(DW^p_B(l_\infty -l_1)\).

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Bulletin of The Iranian Mathematical Society Mathematics-General Mathematics

CiteScore

1.40

自引率

0.00%

发文量

期刊介绍： The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.