• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.125-135
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• 2014

We study the compact intertwining relations for composition operators, whose intertwining operators are Volterra type operators from the weighted Bergman spaces to the weighted Bloch spaces in the unit disk. As consequences, we find a new connection between the weighted Bergman spaces and little weighted Bloch spaces through this relations.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.1
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• pp.13-23
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• 2023

In this paper, we show that for an isometry on a Banach space the analytic spectral subspace coincides with the algebraic spectral subspace. Using this result, we have the following result. Let T be a bounded linear operator with property (δ) on a Banach space X. And let S be an isometry on a Banach space Y . Then every generalized intertwining linear operator θ : X → Y for (S, T) is continuous if and only if the pair (S, T) has no critical eigenvalue.

• Honam Mathematical Journal
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• v.31 no.2
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• pp.219-231
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• 2009

For a mapping satisfying the inequality ${\parallel}{\lambda}f(x)+2{\lambda}f(y)+2f({\lambda}z){\parallel}{\leq}{\parallel}2f({\lambda}({\frac{2}{x}}+y+z)){\parallel}+{\phi}(x,y,z)$, we will study the stability problem of this mapping.

• Journal of English Language & Literature
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• v.57 no.4
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• pp.581-598
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• 2011

The recent revival of phenomenology and aesthetics is deeply connected to the development of neuroscience which studies the nervous system and the brain with particular regard to cognition and memory. How are those fields gathered into building up the basis for the communication not only between human beings but also between humanity and its environment? This paper examines the human mind considered unseparable from the body, with reference to Merleau-Ponty's two major works: Phenomenology of Perception (1962) and The Visible and the Invisible (1968). While reading these texts, I investigate the way he overturns the Cartesian cogito and establishes the body as the ground of perception. According to him, human perception is chiefly obtained through the body rather than consciousness. Influenced by William James, who produced the unique concept of cognition and memory through his experiments with the brain, Merleau-Ponty extends Heideggerian Desein to the field of the embodied mind. James also anticipates Bergson, who regards memory as the product of interaction between consciousness and matter (or the body). The intervention of the body which stores the past experiences makes it impossible for us to capture the present moment in itself. This failure, however, is viewed as positive by Merleau-Ponty because the human body is not only a medium of social interaction, but also that of ecological communion.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.1
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• pp.37-48
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• 2003

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.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.677-686
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• 2016

Algebraic spectral subspaces were introduced by Johnson and Sinclair via a transnite sequence of spaces. Laursen simplified the definition of algebraic spectral subspace. Algebraic spectral subspaces are useful in automatic continuity theory of intertwining linear operators on Banach spaces. In this paper, we characterize algebraic spectral subspaces of operators with finite ascent. From this characterization we show that if T is a generalized scalar operator, then T has finite ascent.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.347-365
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• 1996

Let X and Y be Banach spaces and consider a linear operator $\theta : X \to Y$. The basic automatic continuity problem is to derive the continuity of $\theta$ from some prescribed algebraic conditions. For example, if $\theta : X \to Y$ is a linear operator intertwining with $T \in L(X)$ and $S \in L(Y)$, one may look for algebraic conditions on T and S which force $\theta$ to be continuous.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1263-1272
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• 2008

Let T and S be bounded linear operators on Banach spaces X and y, respectively. A linear map A : X ${\rightarrow}$ y is said to be an intertwiner if AT - SA = 0. In this paper we study the relation between local spectral properties of T and S on the assumption of AT - SA = 0. We give some example of intertwiner with T and S.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.617-627
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• 1994

Algebraic spectral subspaces and admissible operators were introduced by K. B. Laursen and M. M. Neumann in 1988 [L88], [N]. These concepts are useful in automatic continuity problems of intertwining linear operators on Banach spaces. In this paper we characterize the algebraic spectral subspaces of generalized scalar operators. From this characterization we show that generalized scalar operators are admissible. Also we show that doubly power bounded operators are generalized scalar. And using the spectral capacity we show that a generalized scalar operator is decomposable. Then we give an example of an operator which is not admissible but decomposable.

• The Pure and Applied Mathematics
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• v.31 no.2
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• pp.235-249
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• 2024

We obtain a structured class of frames in separable Hilbert spaces which are generalizations of Gabor frames in L²(ℝ) in their construction aspects. For this, the concept of Gabor type unitary systems in [13] is generalized by considering a system of invertible operators in place of unitary systems. Pseudo Gabor like frames and pseudo Gabor frames are introduced and the corresponding frame operators are characterized.