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Weak Hyponomal Composition Operators Induced by a Tree
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  • 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;
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Let g = (V, E, ) be a weighted directed tree, where V is a vertex set, E is an edge set, and is -finite measure on V. The tree g induces a composition operator C on the Hilbert space (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.
directed tree;composition operator;p-hyponormal;p-paranormal;
 Cited by
C. Burnap and I. Jung, Composition operators with weak hyponormality, J. Math. Anal. Appl., 337(2008), 686-694. crossref(new window)

C. Burnap, I. Jung and A. Lambert, Separating partial normality classes with composition operators, J. Operator Theory, 53(2005), 381-397.

G. Exner, I. Jung and M. R. Lee, Block matrix operators and weak hyponormalities, Integr. equ. theory, 65(2009), 345-362. crossref(new window)

T. Furuta, Invitation to linear operators, Taylor & Francis Inc., 2001.

Z. J. Jablonski, I. B. Jung and J. Stochel, On weighted shifts on directed trees, submitted

I. B. Jung, M. R. Lee and P. S. Lim, Gaps of operators, II, Glasgow Math. J., 47(2005), 461-469. crossref(new window)

I. Jung, M. R. Lee and S. Park, Separating classes of composition operators via subnormal condition, Proc. Amer. Math. Soc., 135(2007), 3955-3965. crossref(new window)

M. R. Lee and J. W. Park, Weakly hyponormal composition operators and Embry condition, Kyungpook Math. J., 49(2009), 683-689. crossref(new window)

O. Ore, Theory of graphs, Amer. Math. Soc. Coll. Publ. Vol. XXXVIII, 1962.

M. Rao, Conditional measures and Applications, Marcel Decker, New York 1993.

D. Xia, Spectral theory of hyponormal operators, Birkhauser Verlag, Basel . Boston . Stuttgart, 1983.