Volume 10, Number 1, April 2009, pp. 33-40
Francesco S. De Blasi, Thakyin Hu and Jui-Chi Huang
Key words:
Weak*-topology, Alaoglu theorem, weak*-compactness, hyperspace.
Mathematices Subject Classification: 54A05, 54A20, 54B20.

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	Abstract:
	Let X be a Banach space and X * its dual space. The classical Alaoglu theorem states that closed balls Br* of X * are weak* -compact. Suppose now W* CC (X * ) is the collection of all non-empty weak* -compact, convex subsets of X * i We shall define a certain weak *-topology Ƭ w* on the hyperspace W* CC (X * ) . If $X$ is separable, we shall prove that closed balls Ɓ r* of W* CC (X * ) are weak *-compact ( Ƭ w* -compact).

Weak*-topology and Alaoglu's theorem on hyperspace

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