{"title":"论可数分支图的马图谢克类嵌入障碍","authors":"Ryan Malthaner","doi":"10.1016/j.jmaa.2024.128896","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper we present new proofs of the non-embeddability of countably branching trees into Banach spaces satisfying property <span><math><mo>(</mo><msub><mrow><mi>β</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>)</mo></math></span> and of countably branching diamonds into Banach spaces which are <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-asymptotic midpoint uniformly convex (<em>p</em>-AMUC) for <span><math><mi>p</mi><mo>></mo><mn>1</mn></math></span>. These proofs are entirely metric in nature and are inspired by previous work of Jiří Matoušek. In addition, using this metric method, we succeed in extending these results to metric spaces satisfying certain embedding obstruction inequalities. Finally, we give Tessera-type lower bounds on the compression for a class of Lipschitz embeddings of the countably branching trees into Banach spaces containing <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-asymptotic models for <span><math><mi>p</mi><mo>≥</mo><mn>1</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128896"},"PeriodicalIF":1.2000,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Matoušek-like embedding obstructions of countably branching graphs\",\"authors\":\"Ryan Malthaner\",\"doi\":\"10.1016/j.jmaa.2024.128896\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper we present new proofs of the non-embeddability of countably branching trees into Banach spaces satisfying property <span><math><mo>(</mo><msub><mrow><mi>β</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>)</mo></math></span> and of countably branching diamonds into Banach spaces which are <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-asymptotic midpoint uniformly convex (<em>p</em>-AMUC) for <span><math><mi>p</mi><mo>></mo><mn>1</mn></math></span>. These proofs are entirely metric in nature and are inspired by previous work of Jiří Matoušek. In addition, using this metric method, we succeed in extending these results to metric spaces satisfying certain embedding obstruction inequalities. Finally, we give Tessera-type lower bounds on the compression for a class of Lipschitz embeddings of the countably branching trees into Banach spaces containing <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-asymptotic models for <span><math><mi>p</mi><mo>≥</mo><mn>1</mn></math></span>.</div></div>\",\"PeriodicalId\":50147,\"journal\":{\"name\":\"Journal of Mathematical Analysis and Applications\",\"volume\":\"543 2\",\"pages\":\"Article 128896\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-09-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022247X24008187\",\"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":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24008187","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On Matoušek-like embedding obstructions of countably branching graphs
In this paper we present new proofs of the non-embeddability of countably branching trees into Banach spaces satisfying property and of countably branching diamonds into Banach spaces which are -asymptotic midpoint uniformly convex (p-AMUC) for . These proofs are entirely metric in nature and are inspired by previous work of Jiří Matoušek. In addition, using this metric method, we succeed in extending these results to metric spaces satisfying certain embedding obstruction inequalities. Finally, we give Tessera-type lower bounds on the compression for a class of Lipschitz embeddings of the countably branching trees into Banach spaces containing -asymptotic models for .
期刊介绍:
The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.
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