Abstract
An indispensable tool in the study of deeper structural properties of a Banach space X is its weak topology, i.e., the topology on X of the pointwise convergence on elements of the dual space X *, or the weak * topology on X *, i.e., the topology on X * of the pointwise convergence on elements of X. The topology on X * of the uniform convergence on the family of all convex balanced and weakly compact subsets of X plays also an important role. All those topologies can be efficiently studied in the general framework of topological vector spaces.
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Fabian, M., Habala, P., Hájek, P., Montesinos, V., Zizler, V. (2011). Weak Topologies and Banach Spaces. In: Banach Space Theory. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7515-7_3
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