{"title":"M-serially summing operators on Banach lattices","authors":"Fu Zhang, Hanhan Shen, Zili Chen","doi":"10.1007/s43034-024-00331-2","DOIUrl":null,"url":null,"abstract":"<p>Let <i>E</i>, <i>F</i> be Banach lattices, where <i>E</i> has the disjoint Riesz decomposition property. For a lattice homomorphism <span>\\(T:E\\rightarrow F\\)</span> and a bounded subset <i>A</i> of <i>E</i>, we establish a necessary and sufficient condition under which <i>TA</i> is <i>b</i>-order bounded. Based on this, we study the <i>b</i>-order boundedness of subsets of <i>E</i> and obtain several characterizations of <i>AM</i>-spaces. Furthermore, we introduce and investigate a novel type of operators referred to as <i>M</i>-serially summing operator. The connections of this category of operators with classical notions of operators, such as majorizing operators, preregular operators and serially summing operators, are considered.</p>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s43034-024-00331-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let E, F be Banach lattices, where E has the disjoint Riesz decomposition property. For a lattice homomorphism \(T:E\rightarrow F\) and a bounded subset A of E, we establish a necessary and sufficient condition under which TA is b-order bounded. Based on this, we study the b-order boundedness of subsets of E and obtain several characterizations of AM-spaces. Furthermore, we introduce and investigate a novel type of operators referred to as M-serially summing operator. The connections of this category of operators with classical notions of operators, such as majorizing operators, preregular operators and serially summing operators, are considered.
让 E、F 是巴拿赫晶格，其中 E 具有不相交的 Riesz 分解性质。对于晶格同态（T:E/rightarrow F/）和E的有界子集A，我们建立了TA是b阶有界的必要条件和充分条件。在此基础上，我们研究了 E 子集的 b 阶有界性，并得到了 AM 空间的几个特征。此外，我们还引入并研究了一种新的算子类型，即 M 序列求和算子。我们还考虑了这类算子与经典算子概念（如大化算子、前规则算子和序列求和算子）之间的联系。
期刊介绍：
Annals of Functional Analysis is published by Birkhäuser on behalf of the Tusi Mathematical Research Group.
Ann. Funct. Anal. is a peer-reviewed electronic journal publishing papers of high standards with deep results, new ideas, profound impact, and significant implications in all areas of functional analysis and all modern related topics (e.g., operator theory). Ann. Funct. Anal. normally publishes original research papers numbering 18 or fewer pages in the journal’s style. Longer papers may be submitted to the Banach Journal of Mathematical Analysis or Advances in Operator Theory.
Ann. Funct. Anal. presents the best paper award yearly. The award in the year n is given to the best paper published in the years n-1 and n-2. The referee committee consists of selected editors of the journal.
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