• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.221-226
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• 2007

In this note we set forth three possible definitions of the property of "almost commuting with a compact operator" and discuss an old result of W. Arveson that says that every operator on Hilbert space has the weakest of the three properties. Finally, we discuss some recent progress on the hyperinvariant subspace problem (see the bibliography), and relate it to the concept of almost commuting with a compact operator.

• East Asian mathematical journal
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• v.24 no.1
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• pp.67-79
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• 2008

In this paper, we characterize the chaotic operator order $A\;{\gg}\;C\;{\gg}\;B$. Consequently all other possible characterizations follow easily. Some satellite theorems of the Furuta inequality are naturally given. And finally, using results of characterizing $A\;{\gg}\;C\;{\gg}\;B$, and by the Douglas's majorization and factorization theorem we are able to characterize the chaotic operator order $A\;{\gg}\;B$ in terms of operator equalities.

• 제어로봇시스템학회:학술대회논문집
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• 2002.10a
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• pp.93.4-93
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• 2002

When the GA is applied to optimization problems, it is important to maintain the diversity in designing generation alternation model. Generally, when the diversity is not fully maintained, it is difficult to find good solution, and it is easy to stagnate the early convergenece. In this paper, we propose the Elite Correlation Selection operator (ECS) as a new selection operator for survival. This selection operator aims to keep the diversity of populations and contributes the high searching ability. This selection operator is an extension of selection operator for survival in the Minimal Generation Gap (MGG). In the selection for survival, this selection operator selects one elite individual...

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.599-606
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• 1994

In [1], Cameron and Storvick introduced the analytic operator-valued function space integral. Johnson and Lapidus proved that this integral can be expressed in terms of an integral of operator-valued functions [6]. In this paper, we find some operator-valued Bochner integrable functions and prove that the analytic operator-valued function space integral of a certain function is represented as the Bochner integral of operator-valued functions on some conditions.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.647-650
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• 2009

For a bounded operator T = $U{\mid}T{\mid}$ (polar decomposition), we consider a transform b $\widehat{T}$ = ${\mid}T{\mid}U$ and discuss the convergence of iterated transform of $\widehat{T}$ under the strong operator topology. We prove that such iteration of quasiaffine hyponormal operator converges to a normal operator under the strong operator topology.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.1
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• pp.59-64
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• 2007

In this paper, we will introduce the generalized operator equlibrium problem and generalized operator quasi-equlibrium problem which generalize operator equlibrium problem due to Kazmi and Raouf into multi-valued and quasi-equlibrium problems. Using a Park's fixed point theorem, we will prove a new existence theorem on generalized operator equlibrium problem which serves as a basic existence theorem for various kinds of nonlinear problems.

• Nonlinear Functional Analysis and Applications
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• v.28 no.1
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• pp.81-93
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• 2023

By utilizing a certain Libera integral operator considered on analytic multivalent functions in the unit disk U. Using the hypergeometric function and the Libera integral operator, we included a new convolution operator that expands on some previously specified operators in U, which broadens the scope of certain previously specified operators. We introduced and investigated the properties of new subclasses of functions f (z) ∈ A_p using this operator.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.223-232
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• 2022

The purpose of the paper is to define f-projection operator to develop the f-projection method. The existence of a variational inequality problem is studied using fixed point theorem which establishes the existence of f-projection method. The concept of ρ-projective operator and σ-involutory operator are defined with suitable examples. The relation in between ρ-projective operator and σ-involutory operator are shown. The concept of σ-involutory variational inequality problem is defined and its existence theorem is also established.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.285-295
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• 2013

In this note we present sufficient conditions for the existence of Radon-Nikodym derivatives (RND) of operator valued measures with respect to scalar measures. The RND is characterized by the Bochner integral in the strong operator topology of a strongly measurable operator valued function with respect to a nonnegative finite measure. Using this result we also obtain a characterization of compact sets in the space of operator valued measures. An extension of this result is also given using the theory of Pettis integral. These results have interesting applications in the study of evolution equations on Banach spaces driven by operator valued measures as structural controls.

• Proceedings of the KSR Conference
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• 2005.05a
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• pp.1017-1022
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• 2005

This article studied French case, German case, and England case of rail reform in terms of the relationship between rail infrastructure operator and train operator. Among these three cases there are tie relationship between two different operators backed up by laws. In France the relation between RFF, infrastructure operator, and SNCF, train operator is set up by laws. In Germany the infrastructure operator and train operator form a Konzern and two different operators work with close cooperation. In England SRA, a government authority, plans both infrastructure development and rolling stock demand. From these case studies a conclusion results that there should be a institutional device to maintain close relationship between infrastructure operator and train operator.