{"title":"布洛赫映射的 p-紧密性","authors":"A. Jiménez-Vargas, D. Ruiz-Casternado","doi":"10.1007/s43034-024-00321-4","DOIUrl":null,"url":null,"abstract":"<div><p>Influenced by the concept of a <i>p</i>-compact operator due to Sinha and Karn (Stud Math 150(1): 17–33, 2002), we introduce <i>p</i>-compact Bloch maps of the open unit disk <span>\\(\\mathbb {D}\\subseteq \\mathbb {C}\\)</span> to a complex Banach space <i>X</i>, and obtain its most outstanding properties: surjective Banach ideal property, Möbius invariance, linearisation on the Bloch-free Banach space over <span>\\(\\mathbb {D}\\)</span>, inclusion properties, factorisation of their derivatives, and transposition on the normalized Bloch space. We also present right <i>p</i>-nuclear Bloch maps of <span>\\(\\mathbb {D}\\)</span> to <i>X</i> and study its relation with <i>p</i>-compact Bloch maps.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-024-00321-4.pdf","citationCount":"0","resultStr":"{\"title\":\"p-Compactness of Bloch maps\",\"authors\":\"A. Jiménez-Vargas, D. Ruiz-Casternado\",\"doi\":\"10.1007/s43034-024-00321-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Influenced by the concept of a <i>p</i>-compact operator due to Sinha and Karn (Stud Math 150(1): 17–33, 2002), we introduce <i>p</i>-compact Bloch maps of the open unit disk <span>\\\\(\\\\mathbb {D}\\\\subseteq \\\\mathbb {C}\\\\)</span> to a complex Banach space <i>X</i>, and obtain its most outstanding properties: surjective Banach ideal property, Möbius invariance, linearisation on the Bloch-free Banach space over <span>\\\\(\\\\mathbb {D}\\\\)</span>, inclusion properties, factorisation of their derivatives, and transposition on the normalized Bloch space. We also present right <i>p</i>-nuclear Bloch maps of <span>\\\\(\\\\mathbb {D}\\\\)</span> to <i>X</i> and study its relation with <i>p</i>-compact Bloch maps.</p></div>\",\"PeriodicalId\":48858,\"journal\":{\"name\":\"Annals of Functional Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-02-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s43034-024-00321-4.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Functional Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43034-024-00321-4\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s43034-024-00321-4","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
摘要
受 Sinha 和 Karn 提出的 p-compact 算子概念的影响 (Stud Math 150(1):17-33, 2002)的概念,我们将开放单位盘 \(\mathbb {D}subseteq \mathbb {C}\) 的 p-compact 布洛赫映射引入复巴纳赫空间 X,并得到了它最突出的性质:投射巴纳赫理想性质、莫比乌斯不变性、在 \(\mathbb {D}\) 上无布洛赫的巴纳赫空间上的线性化、包含性质、其导数的因式分解以及在归一化布洛赫空间上的转置。我们还提出了 \(\mathbb {D}\) 到 X 的右 p 核布洛赫映射,并研究了它与 p 紧密布洛赫映射的关系。
Influenced by the concept of a p-compact operator due to Sinha and Karn (Stud Math 150(1): 17–33, 2002), we introduce p-compact Bloch maps of the open unit disk \(\mathbb {D}\subseteq \mathbb {C}\) to a complex Banach space X, and obtain its most outstanding properties: surjective Banach ideal property, Möbius invariance, linearisation on the Bloch-free Banach space over \(\mathbb {D}\), inclusion properties, factorisation of their derivatives, and transposition on the normalized Bloch space. We also present right p-nuclear Bloch maps of \(\mathbb {D}\) to X and study its relation with p-compact Bloch maps.
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.