Weak Hyponomal Composition Operators Induced by a Tree

• Journal title : Kyungpook mathematical journal
• Volume 50, Issue 1,  2010, pp.89-100
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2010.50.1.089
Title & Authors
Weak Hyponomal Composition Operators Induced by a Tree
Lee, Mi-Ryeong; Ahn, Hyo-Gun;

Abstract
Let g = (V, E, $\small{{\mu}}$) be a weighted directed tree, where V is a vertex set, E is an edge set, and $\small{{\mu}}$ is $\small{{\sigma}}$-finite measure on V. The tree g induces a composition operator C on the Hilbert space $\small{l^2}$(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.
Keywords
directed tree;composition operator;p-hyponormal;p-paranormal;
Language
English
Cited by
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