A Generalization of the Isosceles Constant in Banach Spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-04 DOI:10.1007/s00009-024-02654-9

Marco Baronti, Valentina Bertella

引用次数: 0

Abstract

N. Gastinel and J.L. Joly defined the rectangular constant \(\mu \) in Banach spaces using the notion of orthogonality according to Birkhoff and its generalization \(\mu _p\), with \(p\ge 1\). Recently, M. Baronti, E. Casini, and P.L. Papini defined a new constant, the isosceles constant H, in Banach spaces in a very similar way to the rectangular constant, but in this case using the isosceles orthogonality defined by James. In this paper, first of all, we generalize such constant, by defining a new constant \(H_p\) that generalizes the isosceles constant H as well \(\mu _p\) generalizes \(\mu \). After that, we explain its properties, and we give a characterization of Hilbert spaces in terms of it. Moreover a partial characterization of uniformly non-square spaces is given. We conclude by a conjecture about the characterization of uniformly non-square spaces.

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巴拿赫空间中等腰常数的一般化

加斯蒂内尔（N. Gastinel）和乔利（J.L. Joly）使用伯克霍夫的正交概念定义了巴拿赫空间中的矩形常数（\mu \）及其广义化（\(p\ge 1\）。最近，巴朗蒂（M. Baronti）、卡西尼（E. Casini）和帕皮尼（P.L. Papini）在巴拿赫空间中定义了一个新常数，即等腰常数 H，其定义方式与矩形常数非常相似，但在这种情况下使用的是詹姆斯定义的等腰正交性。在本文中，首先，我们通过定义一个新的常数 \(H_p\)来概括这个常数，这个常数概括了等腰常数 H 以及 \(\mu_p\)概括了 \(\mu\)。之后，我们解释了它的性质，并用它给出了希尔伯特空间的特征。此外，我们还给出了均匀非平方空间的部分特征。最后，我们提出一个关于均匀非方差空间特征的猜想。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.