Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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CONTINUITY OF LINEAR OPERATOR INTERTWINING WITH DECOMPOSABLE OPERATORS AND PURE HYPONORMAL OPERATORS

  • Park, Sung-Wook (Department of Applied Mathematics Kumoh National University of Technology) ;
  • Han, Hyuk (Department of Mathematics Seonam University) ;
  • Park, Se Won (Department of Mathematics Seonam University)
  • Received : 2003.05.06
  • Published : 2003.06.30
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Abstract

In this paper, we show that for a pure hyponormal operator the analytic spectral subspace and the algebraic spectral subspace are coincide. Using this result, we have the following result: Let T be a decomposable operator on a Banach space X and let S be a pure hyponormal operator on a Hilbert space H. Then every linear operator ${\theta}:X{\rightarrow}H$ with $S{\theta}={\theta}T$ is automatically continuous.

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