Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON OPERATORS T COMMUTING WITH CT C WHERE C IS A CONJUGATION

  • Cho, Muneo (Department of Mathematics Kanagawa University) ;
  • Ko, Eungil (Department of Mathematics Ewha Womans University) ;
  • Lee, Ji Eun (Department of Mathematics and Statistics Sejong University)
  • Received : 2019.01.15
  • Accepted : 2019.09.19
  • Published : 2020.01.31
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Abstract

In this paper, we study the properties of T satisfying [CTC, T] = 0 for some conjugation C where [R, S] := RS - SR. In particular, we show that if T is normal, then [CTC, C] = 0. Moreover, the class of operators T satisfy [CTC, T] = 0 is norm closed. Finally, we prove that if T is complex symmetric, then T is binormal if and only if [C|T|C, |T|] = 0.

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References

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