{"title":"Monotonicity properties of weighted geometric symmetrizations","authors":"Katarina Bogdanović, Aljoša Peperko","doi":"arxiv-2408.04357","DOIUrl":null,"url":null,"abstract":"We prove new monotonicity properties for spectral radius, essential spectral\nradius, operator norm, Hausdorff measure of non-compactness and numerical\nradius of products and sums of weighted geometric symmetrizations of positive\nkernel operators on $L^2$. To our knowledge, several proved properties are new\neven in the finite dimensional case.","PeriodicalId":501036,"journal":{"name":"arXiv - MATH - Functional Analysis","volume":"368 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.04357","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We prove new monotonicity properties for spectral radius, essential spectral
radius, operator norm, Hausdorff measure of non-compactness and numerical
radius of products and sums of weighted geometric symmetrizations of positive
kernel operators on $L^2$. To our knowledge, several proved properties are new
even in the finite dimensional case.
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