Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Weak Hyponomal Composition Operators Induced by a Tree

  • Lee, Mi-Ryeong (Faculty of Liberal Education, Kyungpook National University) ;
  • Ahn, Hyo-Gun (Department of Mathematics, College of Natural Sciences, Kyungpook National University)
  • Received : 2009.10.23
  • Accepted : 2010.01.25
  • Published : 2010.03.31
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Abstract

Let g = (V, E, ${\mu}$) be a weighted directed tree, where V is a vertex set, E is an edge set, and ${\mu}$ is ${\sigma}$-finite measure on V. The tree g induces a composition operator C on the Hilbert space $l^2$(V). Hand-type directed trees are defined and characterized the weak hyponormalities of such C in this note. Also some additional related properties are discussed. In addition, some examples related to directed hand-type trees are provided to separate classes of weak-hyponormal operators.

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References

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