{"title":"Banach-Mazur非致密性数","authors":"G. García, G. Mora","doi":"10.1007/s43036-024-00408-8","DOIUrl":null,"url":null,"abstract":"<div><p>In the present paper, based on the so called degree of nondensifiability (DND), we introduce the concept of Banach–Mazur nondensifiability number of two given Banach spaces and prove that such a number is an optimal lower bound for the well known Banach–Mazur distance. For a given infinite dimensional Banach space, we also introduce a new constant. We demonstrate a relationship between this constant and the Banach–Mazur distance.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Banach–Mazur nondensifiability number\",\"authors\":\"G. García, G. Mora\",\"doi\":\"10.1007/s43036-024-00408-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In the present paper, based on the so called degree of nondensifiability (DND), we introduce the concept of Banach–Mazur nondensifiability number of two given Banach spaces and prove that such a number is an optimal lower bound for the well known Banach–Mazur distance. For a given infinite dimensional Banach space, we also introduce a new constant. We demonstrate a relationship between this constant and the Banach–Mazur distance.</p></div>\",\"PeriodicalId\":44371,\"journal\":{\"name\":\"Advances in Operator Theory\",\"volume\":\"10 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-12-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Operator Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s43036-024-00408-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-024-00408-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
In the present paper, based on the so called degree of nondensifiability (DND), we introduce the concept of Banach–Mazur nondensifiability number of two given Banach spaces and prove that such a number is an optimal lower bound for the well known Banach–Mazur distance. For a given infinite dimensional Banach space, we also introduce a new constant. We demonstrate a relationship between this constant and the Banach–Mazur distance.
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