• 대한수학회보
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• 제52권1호
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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.

• 대한수학회보
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• 제50권1호
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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.