The unit ball of the Hilbert space in its weak topology

2009/03/01 by Antonio Avilés · 1 citation
Mathematics · #math.FA #math.GN #msc:46B26 #msc:46B50 #msc:46C05 #msc:54B30 #msc:54D15.

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published as Proc. Am. Math. Soc. 135, No. 3, 833-836 (2007)

arxiv created 2009/03/01 · arxiv updated 2009/12/01

Abstract

We show that the unit ball of a Hilbert space in its weak topology is a continuous image of the countable power of the Alexandroff compactification of a discrete set, and we deduce some combinatorial properties of its lattice of open sets which are not shared by the balls of other equivalent norms when the space is nonseparable.

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