{"title":"PROPERTIES OF OPERATOR MATRICES","authors":"I. An, E. Ko, J. Lee","doi":"10.4134/JKMS.J190439","DOIUrl":null,"url":null,"abstract":"Let S be the collection of the operator matrices ( A C Z B ) where the range of C is closed. In this paper, we study the properties of operator matrices in the class S. We first explore various local spectral relations, that is, the property (β), decomposable, and the property (C) between the operator matrices in the class S and their component operators. Moreover, we investigate Weyl and Browder type spectra of operator matrices in the class S, and as some applications, we provide the conditions for such operator matrices to satisfy a-Weyl’s theorem and a-Browder’s theorem, respectively.","PeriodicalId":49993,"journal":{"name":"Journal of the Korean Mathematical Society","volume":"57 1","pages":"893-913"},"PeriodicalIF":0.5000,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Korean Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4134/JKMS.J190439","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
Let S be the collection of the operator matrices ( A C Z B ) where the range of C is closed. In this paper, we study the properties of operator matrices in the class S. We first explore various local spectral relations, that is, the property (β), decomposable, and the property (C) between the operator matrices in the class S and their component operators. Moreover, we investigate Weyl and Browder type spectra of operator matrices in the class S, and as some applications, we provide the conditions for such operator matrices to satisfy a-Weyl’s theorem and a-Browder’s theorem, respectively.
设S是算子矩阵(A C Z B)的集合，其中C的值域是封闭的。本文研究了S类算子矩阵的性质。首先探讨了S类算子矩阵与其组成算子之间的各种局域谱关系，即性质(β)、可分解性和性质(C)。此外，我们研究了S类算子矩阵的Weyl和Browder型谱，并作为一些应用，给出了这类算子矩阵分别满足a-Weyl定理和a-Browder定理的条件。
期刊介绍：
This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).
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