{"title":"Non-normable spaces of analytic functions","authors":"Iván Jiménez, Dragan Vukotić","doi":"arxiv-2407.21212","DOIUrl":null,"url":null,"abstract":"For each value of $p$ such that $0<p<1$, we give a specific example of two\nfunctions in the Hardy space $H^p$ and in the Bergman space $A^p$ that do not\nsatisfy the triangle inequality. For Hardy spaces, this provides a much simpler\nproof than the one due to Livingston that involves abstract functional analysis\narguments and an approximation theorem. For Bergman spaces, we have not been\nable to locate any examples or proofs in the existing literature.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"65 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.21212","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}