• Korean Journal of Mathematics
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• v.13 no.2
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• pp.255-273
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• 2005

We characterize Gaussian cotype X operators acting between Banach spaces, where X is a Banach sequence space. Further we give an extensive presentation of results on the connections between cotype and summing operators.

• Korean Journal of Mathematics
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• v.13 no.1
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• pp.61-82
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• 2005

We characterize Gaussian cotype X operators acting between Banach spaces, where X is a Banach sequence space. Further we give an extensive presentation of results on the connections between cotype and summing operators.

• Journal of the Korean Mathematical Society
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• v.47 no.5
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• pp.899-924
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• 2010

In the paper we introduce averages of each type and use these averages to construct examples of weakly compact operators on the space C ($\Omega$) for which the necessary and sufficient conditions that they be compact, absolutely summing or nuclear are distinct. A great number of concrete examples, in various situations, are given.

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.147-154
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• 2022

In this article, we prove that an absolutely summing operator on 𝓛^λ₁ spaces has a lifting under the conditions that a target Banach space is a quotient of reflexive Banach subspaces.

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.967-986
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• 2017

We give the necessary condition for an operator defined on a cartesian product of $c_0(\mathcal{X})$ spaces to be summing or dominated and we show that for the multiplication operators this condition is also sufficient. By using these results, we show that ${\Pi}_s(c_0,{\ldots},c_0;c_0)$ contains a copy of $l_s(l^m_2{\mid}m{\in}\mathbb{N})$ for s > 2 or a copy of $1_s(l^m_1{\mid}{\in}\mathbb{N})$, for any $l{\leq}S$ < ${\infty}$. Also ${\Delta}_{s_1,{\ldots},s_n}(c_0,{\ldots},c_0;c_0)$ contains a copy of $l_{{\upsilon}_n(s_1,{\ldots},s_n)}$ if ${\upsilon}_n(s_1,{\ldots},s_n){\leq}2$ or a copy of $l_{{\upsilon}_n(s_1,{\ldots},s_n)}(l^m_2{\mid}m{\in}\mathbb{N})$ if 2 < ${\upsilon}_n(s_1,{\ldots},s_n)$, where ${\frac{1}{{\upsilon}_n(s_1,{\ldots},s_n})}={\frac{1}{s_1}}+{\cdots}+{\frac{1}{s_n}}$. We find also the necessary and sufficient conditions for bilinear operators induced by some method of summability to be 1-summing or 2-dominated.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.447-456
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• 2015

In this paper we show that some operators defined on the Banach space with an unconditional basis and $L^1({\mu})$ into a Banach space with the RNP have liftable operators.

• Communications of the Korean Mathematical Society
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• v.16 no.1
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• pp.119-124
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• 2001

In the paper we show that some operators defined on L$^1$($\mu$) and on C(K) into Banach space with the RNP have the lifting property.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.645-655
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• 2019

In this article, we show that the nuclear operator defined on Banach space has an extending and lifting operator. Also we give new proofs of the well known facts which were given $Pelcz{\acute{y}}nski$ theorem for complemented subspaces of ${\ell}_1$ and Lewis and Stegall's theorem for complemented subspaces of $L_1({\mu})$.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.19 no.6
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• pp.14-25
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• 2020

This research proposes a methodology to evaluate the rationality of passengers' route choice who make trips within Seoul metropolitan subway based on smart card data. The rationality of user route choice is divided into the degree of determinacy and similarity concepts as basic principle. Determinacy is the degree to which the route selected by the passenger is identical to the system optimal path. Similarity indicates the degree to which the route is similar to the system optimal path. The K-path search method is used for path enumeration, which allows for measurement of determinacy. To assess determinacy within similarity, transfer tag data of private operators is used. Consequently, the concept of similarity applied to the model is such that the passenger's path choice is identical to the path taken using the tag reader. Results show that the determinacy of appearance of the shortest path (K=1) is 90.4%, while the similarity of appearance as K=(2-10) is 7.9%, summing to 98.3%. This indicates that trips on the metropolitan subway network are being rationally explained. 1.7% of irrational trips are attributed to the unexplainable error term that occurs due to the diversity of passengers.