{"title":"论 ℓ1$\\ell _1$ 上有界型对称解析函数代数的谱","authors":"Iryna Chernega, Pablo Galindo, Andriy Zagorodnyuk","doi":"10.1002/mana.202300415","DOIUrl":null,"url":null,"abstract":"<p>We obtain a complete description of the spectrum of the Fréchet algebra of symmetric analytic functions bounded on balls on the sequence space <span></span><math>\n <semantics>\n <msub>\n <mi>ℓ</mi>\n <mn>1</mn>\n </msub>\n <annotation>$\\ell _1$</annotation>\n </semantics></math>. This is achieved after proving that on the analogous algebra for <span></span><math>\n <semantics>\n <msub>\n <mi>ℓ</mi>\n <mi>p</mi>\n </msub>\n <annotation>$\\ell _p$</annotation>\n </semantics></math>, <span></span><math>\n <semantics>\n <mrow>\n <mn>1</mn>\n <mo>≤</mo>\n <mi>p</mi>\n <mo><</mo>\n <mi>∞</mi>\n </mrow>\n <annotation>$1\\le p &lt;\\infty$</annotation>\n </semantics></math>, the radius function of any evaluation homomorphism <span></span><math>\n <semantics>\n <mrow>\n <msub>\n <mi>δ</mi>\n <mi>x</mi>\n </msub>\n <mo>,</mo>\n <mspace></mspace>\n <mi>x</mi>\n <mo>∈</mo>\n <msub>\n <mi>ℓ</mi>\n <mi>p</mi>\n </msub>\n </mrow>\n <annotation>$\\delta _x, \\nobreakspace x \\in \\ell _p$</annotation>\n </semantics></math>, coincides with the norm of <span></span><math>\n <semantics>\n <mi>x</mi>\n <annotation>$x$</annotation>\n </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"297 10","pages":"3835-3846"},"PeriodicalIF":0.8000,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the spectrum of the algebra of bounded-type symmetric analytic functions on \\n \\n \\n ℓ\\n 1\\n \\n $\\\\ell _1$\",\"authors\":\"Iryna Chernega, Pablo Galindo, Andriy Zagorodnyuk\",\"doi\":\"10.1002/mana.202300415\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We obtain a complete description of the spectrum of the Fréchet algebra of symmetric analytic functions bounded on balls on the sequence space <span></span><math>\\n <semantics>\\n <msub>\\n <mi>ℓ</mi>\\n <mn>1</mn>\\n </msub>\\n <annotation>$\\\\ell _1$</annotation>\\n </semantics></math>. This is achieved after proving that on the analogous algebra for <span></span><math>\\n <semantics>\\n <msub>\\n <mi>ℓ</mi>\\n <mi>p</mi>\\n </msub>\\n <annotation>$\\\\ell _p$</annotation>\\n </semantics></math>, <span></span><math>\\n <semantics>\\n <mrow>\\n <mn>1</mn>\\n <mo>≤</mo>\\n <mi>p</mi>\\n <mo><</mo>\\n <mi>∞</mi>\\n </mrow>\\n <annotation>$1\\\\le p &lt;\\\\infty$</annotation>\\n </semantics></math>, the radius function of any evaluation homomorphism <span></span><math>\\n <semantics>\\n <mrow>\\n <msub>\\n <mi>δ</mi>\\n <mi>x</mi>\\n </msub>\\n <mo>,</mo>\\n <mspace></mspace>\\n <mi>x</mi>\\n <mo>∈</mo>\\n <msub>\\n <mi>ℓ</mi>\\n <mi>p</mi>\\n </msub>\\n </mrow>\\n <annotation>$\\\\delta _x, \\\\nobreakspace x \\\\in \\\\ell _p$</annotation>\\n </semantics></math>, coincides with the norm of <span></span><math>\\n <semantics>\\n <mi>x</mi>\\n <annotation>$x$</annotation>\\n </semantics></math>.</p>\",\"PeriodicalId\":49853,\"journal\":{\"name\":\"Mathematische Nachrichten\",\"volume\":\"297 10\",\"pages\":\"3835-3846\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematische Nachrichten\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mana.202300415\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematische Nachrichten","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mana.202300415","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the spectrum of the algebra of bounded-type symmetric analytic functions on
ℓ
1
$\ell _1$
We obtain a complete description of the spectrum of the Fréchet algebra of symmetric analytic functions bounded on balls on the sequence space . This is achieved after proving that on the analogous algebra for , , the radius function of any evaluation homomorphism , coincides with the norm of .
期刊介绍：
Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
