Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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RIESZ PROJECTIONS FOR A NON-HYPONORMAL OPERATOR

  • Lee, Jae Won (Department of Applied Mathematics Kumoh National Institute of Technology) ;
  • Jeon, In Ho (Department of Mathematics Education Seoul National University of Education)
  • Received : 2016.02.06
  • Accepted : 2016.02.29
  • Published : 2016.03.30
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Abstract

J. G. Stampfli proved that if a bounded linear operator T on a Hilbert space ${\mathfrak{H}}$ satisfies ($G_1$) property, then the Riesz projection $P_{\lambda}$ associated with ${\lambda}{\in}iso{\sigma}$(T) is self-adjoint and $P_{\lambda}{\mathfrak{H}}=(T-{\lambda})^{-1}(0)=(T^*-{\bar{\lambda}})^{-1}(0)$. In this note we show that Stampfli''s result is generalized to an nilpotent extension of an operator having ($G_1$) property.

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References

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