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拟相似算子的右本质谱的连通分支 被引量：1

Components of the Right Essential Spectrum of Quasisimilar Operators
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摘要 设算子S和T拟相似,通过引进RT类算子、R类算子和RR类算子的概念,给出右本质谱σre(S)的连通分支与σre(T)相交的充分条件和必要条件以及σre(S)的连通分支与本质谱盯σe(T)的某些子集的相交关系,并给出算子是属于RT类算子和RR类算子的充分条件和必要条件. Let S and T be quasisimilar operators. By introducing the concepts of the RT-class operator, the R-class operator and the RR-class operator, this paper gives some sufficient and necessary conditions under which each component of σre（S） intersects σre（T）, and gives some sufficient conditions under which each component of σre（S） intersets some subsets of σe（T）, and also gives some sufficient and necessary conditions under which an operator is an RT-class operator and an RR-class operator respectively.
作者 苏维钢
机构地区 河北师范大学数学与信息科学学院
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2005年第5期993-998,共6页 Acta Mathematica Sinica：Chinese Series
基金 国家自然科学基金资助项目(10471025)福建省教育厅基金资助项目(JA04170)
关键词 有界线性算子 拟相似 右本质谱 Bounded linear operator Quasisimilarity Right essential spectrum
分类号 O177.7 [理学—基础数学]
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参考文献8

  • 1Sz-Nagy B., Foias C., Harmonic analysis of operators on Hilbert spaces, Amsterdam: North-Holland, 1970.
  • 2Hoover T. B., Quasisimilarity of operators, Illinois J. Math., 1972, 16: 672-686.
  • 3Fialkow L. A., A note on quasisimilarity of operators, Acta Sci. Math., 1977, 39: 67-85.
  • 4Herrero D. A., On the essential spectra of quasisimilar operators, Canad. J. Math., 1988, 40: 1436-1457.
  • 5Kato T., Perturbation theory for linear operators, New York: Springer-Verlag, 1966.
  • 6Yan Z. K., Some results on the quasisimilarity of operators, Chinese Science Bulletin, 1990, 35(4): 241-243(in Chinese).
  • 7Yan Z. K., The quasisimilarity of operators and the problem of Fialkow, Chinese Science Bulletin, 1988,33(21): 1677-1678 (in Chinese).
  • 8Herrero D. A., A dense set of operators quasisimilar to normal + compact, Proc. Amer. Math. Soc., 1987,100: 641-646.

同被引文献9

  • 1钟怀杰.Banach空间结构和算子理想[M].北京:科学出版社,2005.
  • 2Sz-Nagy B,Foias C.Harmonic Analysis of Operators on Hilbert Spaces[M].Amsterdam:North-Holland,1970.
  • 3Jeon I H.Weyl's theorem and quasi-similarity[J].Integral Equations and Operator Theory,2001,39:214-221.
  • 4Duggal B P.Quasi-similar p-hyponormal operators[J].Integral Equations and Operator Theory,1996,26:338-345.
  • 5Herrero D A.On the essential spectra of quasisimilar operators[J].Canad J Math,1988,40:1436-1457.
  • 6Karo T.Perturbation Theory for Linear Operators[M].New York:Springer-Verlag,1966.
  • 7Rudin W.Real and Complex Analysis[M].New York:McGraw-Hill,1987.
  • 8Fialkow L A.A note on the operator X→AX-XB[J].Trans Amer Math Soc,1978,243:147-168.
  • 9Williams L R.Equality of essential spectra of quasisimilar quasinormal operators[J].Integral Equations and Operator Theory,1980,3:57-69.

引证文献1

数学学报（中文版）
2005年 第5期

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