{"title":"Canonical embedding of Lipschitz-free p-spaces","authors":"Marek Cúth, Tomáš Raunig","doi":"10.1007/s43037-024-00339-9","DOIUrl":null,"url":null,"abstract":"<p>We find a new finite algorithm for evaluation of Lipschitz-free <i>p</i>-space norm in finite-dimensional Lipschitz-free <i>p</i>-spaces. We use this algorithm to deal with the problem of whether given <i>p</i>-metric spaces <span>\\(\\mathcal {N}\\subset \\mathcal {M},\\)</span> the canonical embedding of <span>\\(\\mathcal {F}_p(\\mathcal {N})\\)</span> into <span>\\(\\mathcal {F}_p(\\mathcal {M})\\)</span> is an isomorphism. The most significant result in this direction is that the answer is positive if <span>\\(\\mathcal {N}\\subset \\mathcal {M}\\)</span> are metric spaces.</p>","PeriodicalId":55400,"journal":{"name":"Banach Journal of Mathematical Analysis","volume":"68 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Banach Journal of Mathematical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s43037-024-00339-9","RegionNum":2,"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
We find a new finite algorithm for evaluation of Lipschitz-free p-space norm in finite-dimensional Lipschitz-free p-spaces. We use this algorithm to deal with the problem of whether given p-metric spaces \(\mathcal {N}\subset \mathcal {M},\) the canonical embedding of \(\mathcal {F}_p(\mathcal {N})\) into \(\mathcal {F}_p(\mathcal {M})\) is an isomorphism. The most significant result in this direction is that the answer is positive if \(\mathcal {N}\subset \mathcal {M}\) are metric spaces.
期刊介绍:
The Banach Journal of Mathematical Analysis (Banach J. Math. Anal.) is published by Birkhäuser on behalf of the Tusi Mathematical Research Group.
Banach J. Math. 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 operator theory and all modern related topics. Banach J. Math. Anal. normally publishes survey articles and original research papers numbering 15 pages or more in the journal’s style. Shorter papers may be submitted to the Annals of Functional Analysis or Advances in Operator Theory.