{"title":"加权几何对称的单调性特性","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":"{\"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}","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}
Monotonicity properties of weighted geometric symmetrizations
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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