{"title":"Subordination and related inequalities on a C⁎−algebra","authors":"A.K. Mishra , P. Gochhayat","doi":"10.1016/j.jmaa.2025.129365","DOIUrl":null,"url":null,"abstract":"<div><div>Let <strong>X</strong> be a <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra, <span><math><mi>x</mi><mo>∈</mo><mi>X</mi></math></span> and <span><math><mo>‖</mo><mi>x</mi><mo>‖</mo><mo><</mo><mn>1</mn></math></span>. For a complex valued function <em>f</em>, which is analytic in <span><math><mi>U</mi><mo>=</mo><mo>{</mo><mi>λ</mi><mo>∈</mo><mi>C</mi><mo>:</mo><mo>|</mo><mi>λ</mi><mo>|</mo><mo><</mo><mn>1</mn><mo>}</mo></math></span> let <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> be defined by the following integral: <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><msub><mrow><mo>∫</mo></mrow><mrow><mi>Γ</mi></mrow></msub><mi>f</mi><mo>(</mo><mi>λ</mi><mo>)</mo><msup><mrow><mo>(</mo><mi>λ</mi><mi>e</mi><mo>−</mo><mi>x</mi><mo>)</mo></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mspace></mspace><mi>d</mi><mi>λ</mi></math></span>, where Γ is a positively oriented rectifiable simple closed contour in <span><math><mi>U</mi></math></span> that <em>surrounds</em> <span><math><mi>σ</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span>, the spectrum of <em>x</em>. In this paper Schwarz's lemma, Harnack's inequalities and results related to subordination are obtained for <span><math><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"547 2","pages":"Article 129365"},"PeriodicalIF":1.2000,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X25001465","RegionNum":3,"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
Let X be a -algebra, and . For a complex valued function f, which is analytic in let be defined by the following integral: , where Γ is a positively oriented rectifiable simple closed contour in that surrounds , the spectrum of x. In this paper Schwarz's lemma, Harnack's inequalities and results related to subordination are obtained for .
期刊介绍:
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