• 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.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.69-83
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• 2015

In this paper we introduce and study the separable weak bounded approximation properties which is strictly stronger than the approximation property and but weaker than the bounded approximation property. It provides new sufficient conditions for the metric approximation property for a dual Banach space.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1579-1586
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• 2015

In this paper we investigate the barrellednes of some spaces of X-valued measures, X being a barrelled normed space, and provide examples of non barrelled spaces of bounded linear operators from a Banach space X into a barrelled normed space Y, equipped with the uniform convergence topology.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.161-173
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• 2013

This paper is concerned with the space $\mathcal{K}_{w^*}(X^*,Y)$ of $weak^*$ to weak continuous compact operators from the dual space $X^*$ of a Banach space X to a Banach space Y. We show that if $X^*$ or $Y^*$ has the Radon-Nikod$\acute{y}$m property, $\mathcal{C}$ is a convex subset of $\mathcal{K}_{w^*}(X^*,Y)$ with $0{\in}\mathcal{C}$ and T is a bounded linear operator from $X^*$ into Y, then $T{\in}\bar{\mathcal{C}}^{{\tau}_{\mathcal{c}}}$ if and only if $T{\in}\bar{\{S{\in}\mathcal{C}:{\parallel}S{\parallel}{\leq}{\parallel}T{\parallel}\}}^{{\tau}_{\mathcal{c}}}$, where ${\tau}_{\mathcal{c}}$ is the topology of uniform convergence on each compact subset of X, moreover, if $T{\in}\mathcal{K}_{w^*}(X^*, Y)$, here $\mathcal{C}$ need not to contain 0, then $T{\in}\bar{\mathcal{C}}^{{\tau}_{\mathcal{c}}}$ if and only if $T{\in}\bar{\mathcal{C}}$ in the topology of the operator norm. Some properties of $\mathcal{K}_{w^*}(X^*,Y)$ are presented.