Korean Journal of Mathematics

  • 제19권1호
  • /
  • Pages.61-64
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  • 2011
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  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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A STUDY ON OPERATORS SATISFYING |T2| ≥ |T*|2

  • Lee, Jae Won (Department of Applied Mathematics Kumoh National Institute of Technology) ;
  • Jeon, In Ho (Department of Mathematics Education Seoul National University of Education)
  • 투고 : 2011.02.17
  • 심사 : 2011.03.10
  • 발행 : 2011.03.30
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초록

Let $\mathcal{A}^*$ denotes the class of operators satisfying $|T^2|{\geq}|T^*|^2$. In this paper, we show if the restriction to a non-trivial invariant subspace $\mathcal{M}$ of an operator $T{\in}\mathcal{A}^*$ is normal, then $\mathcal{M}$ reduces T.

키워드

참고문헌

  1. S. C. Arora and J. K. Thukral, On a class of operators, Glas. Mat. Ser. III 21(1986), 381-386.
  2. B. P. Dugall, I. H. Jeon, and I. H. Kim, On *-paranormal contractions and properties for *-class A operators, preprint(2010). https://doi.org/10.1016/j.laa.2011.06.002
  3. T. Furuta, Invitation to Linear Operators, Taylor and Francis, London 2001.
  4. P. B. Halmos, A Hilbert Space Problem Book, Van Nostrand, Princeton 1967.
  5. I. H. Jeon and I. H. Kim, On operators satisfying ${T^*}{\mid}{T^2}{\mid}{T}{\geq}{\mid}{T^*}{\mid}{T}{\mid}{^2T}$, Linear Algebra Appl. 418 (2006), 854-862. https://doi.org/10.1016/j.laa.2006.02.040
  6. K. B. Laursen and M. N. Neumann, Introduction to local spectral theory, Clarendon Press, Oxford 2000.