{"title":"On p-height orthogonality and characterization of inner product spaces","authors":"Somaye Heidarirad, Ruhollah Jahanipur, Mahdi Dehghani","doi":"10.1016/j.jmaa.2024.128964","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we introduce and study the concept of <em>p</em>-height orthogonality in real normed linear spaces. This orthogonality generalizes the well-known Singer and height orthogonalities. First, we investigate main properties of this type of orthogonality. Then, variety of examples are presented to illustrate the relationship between <em>p</em>-height orthogonality and other previously defined (e.g., isosceles, Singer, height and Birkhoff-James) orthogonalities. Also we investigate the existence properties of this new notion of orthogonality. In particular, <em>α</em>-existence property is established and some interesting bounds for the values of <em>α</em> are obtained. Moreover, some characterizations of inner product spaces are given in terms of <em>p</em>-height orthogonality and its relation with Pythagorean and Birkhoff-James orthogonalities.</div></div>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24008862","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we introduce and study the concept of p-height orthogonality in real normed linear spaces. This orthogonality generalizes the well-known Singer and height orthogonalities. First, we investigate main properties of this type of orthogonality. Then, variety of examples are presented to illustrate the relationship between p-height orthogonality and other previously defined (e.g., isosceles, Singer, height and Birkhoff-James) orthogonalities. Also we investigate the existence properties of this new notion of orthogonality. In particular, α-existence property is established and some interesting bounds for the values of α are obtained. Moreover, some characterizations of inner product spaces are given in terms of p-height orthogonality and its relation with Pythagorean and Birkhoff-James orthogonalities.
本文介绍并研究了实规范线性空间中 p 高度正交性的概念。这种正交性概括了众所周知的辛格正交性和高度正交性。首先，我们研究了这种正交性的主要性质。然后，举出各种例子来说明 p 高度正交性与之前定义的其他正交性（如等腰、辛格、高度和伯克霍夫-詹姆斯）之间的关系。此外，我们还研究了这一新的正交概念的存在性。特别是，我们建立了 α 存在性，并得到了 α 值的一些有趣界限。此外，根据 p 高度正交性及其与毕达哥拉斯正交性和伯克霍夫-詹姆斯正交性的关系，给出了内积空间的一些特征。
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.
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