{"title":"Riesz idempotent, spectral mapping theorem and Weyl's theorem for (m,n)*-paranormal operators","authors":"S. Ram, P. Dharmarha","doi":"10.2298/fil2110293d","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we show that the spectral mapping theorem holds for ( m , n ) * {(m,n)^{*}} -paranormal operators. We also exhibit the self-adjointness of the Riesz idempotent E λ {E_{\\lambda}} of ( m , n ) * {(m,n)^{*}} -paranormal operators concerning for each isolated point λ of σ ( T ) {\\sigma(T)} . Moreover, we show Weyl’s theorem for ( m , n ) * {(m,n)^{*}} -paranormal operators and f ( T ) {f(T)} for every f ∈ ℋ ( σ ( T ) ) {f\\in\\mathcal{H}(\\sigma(T))} . Furthermore, we investigate the class of totally ( m , n ) * {(m,n)^{*}} -paranormal operators and show that Weyl’s theorem holds for operators in this class.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Random Operators and Stochastic Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2298/fil2110293d","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract In this paper, we show that the spectral mapping theorem holds for ( m , n ) * {(m,n)^{*}} -paranormal operators. We also exhibit the self-adjointness of the Riesz idempotent E λ {E_{\lambda}} of ( m , n ) * {(m,n)^{*}} -paranormal operators concerning for each isolated point λ of σ ( T ) {\sigma(T)} . Moreover, we show Weyl’s theorem for ( m , n ) * {(m,n)^{*}} -paranormal operators and f ( T ) {f(T)} for every f ∈ ℋ ( σ ( T ) ) {f\in\mathcal{H}(\sigma(T))} . Furthermore, we investigate the class of totally ( m , n ) * {(m,n)^{*}} -paranormal operators and show that Weyl’s theorem holds for operators in this class.