• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.1-20
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• 2004

Let A be a uniform algebra, and let $\phi$ be a self-map of the spectrum $M_A$ of A that induces a composition operator $C_{\phi}$, on A. It is shown that the image of $M_A$ under some iterate ${\phi}^n$ of \phi is hyperbolically bounded if and only if \phi has a finite number of attracting cycles to which the iterates of $\phi$ converge. On the other hand, the image of the spectrum of A under $\phi$ is not hyperbolically bounded if and only if there is a subspace of $A^{**}$ "almost" isometric to ${\ell}_{\infty}$ on which ${C_{\phi}}^{**}$ "almost" an isometry. A corollary of these characterizations is that if $C_{\phi}$ is weakly compact, and if the spectrum of A is connected, then $\phi$ has a unique fixed point, to which the iterates of $\phi$ converge. The corresponding theorem for compact composition operators was proved in 1980 by H. Kamowitz [17].

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.627-645
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• 2017

In this paper, we characterize the boundedness, compactness and essential norm of products of differentiation and composition operators from the Bloch space and weighted Dirichlet spaces to analytic Morrey type spaces.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1187-1193
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• 2014

We will characterize the boundedness and compactness of weighted composition operators on the minimal M$\ddot{o}$bius invariant space.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1005-1013
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• 2014

Let ${\phi}$ be an analytic self map of the open unit disc D. In this paper, we study the composition operator $C_{\phi}$ from the Bergman space on D to the Hardy space on D.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.125-130
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• 2016

A finite rank difference of two composition operators is studied on a Hilbert Lebesgue space or a Hilbert Hardy space.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.89-100
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• 2010

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.

• Bulletin of the Korean Mathematical Society
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• v.54 no.1
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• pp.187-198
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• 2017

We obtain some necessary and sufficient conditions for the boundedness of the composition operators between weighted Bergman spaces of logarithmic weights. In terms of the conditions for the boundedness, we compute the essential norm of the composition operators.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.169-176
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• 2015

A sequence of composition operators on Hardy space is considered. We prove that, by numerical range properties, it is SOT-convergence but not converge.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.413-418
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• 2004

Invertible and isometric composition operators acting on vector-valued Hardy space $H^2$(E) are characterized.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1063-1079
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• 2017

Two standard Bessel sequences in a Hilbert $C^*$-module are approximately duals if the distance (with respect to the norm) between the identity operator on the Hilbert $C^*$-module and the operator constructed by the composition of the synthesis and analysis operators of these Bessel sequences is strictly less than one. In this paper, we introduce (a, m)-approximate duality using the distance between the identity operator and the operator defined by multiplying the Bessel multiplier with symbol m by an element a in the center of the $C^*$-algebra. We show that approximate duals are special cases of (a, m)-approximate duals and we generalize some of the important results obtained for approximate duals to (a, m)-approximate duals. Especially we study perturbations of (a, m)-approximate duals and (a, m)-approximate duals of modular Riesz bases.