The unit ball of the Hilbert space in its weak topology

Avilés, Antonio

doi:10.1090/S0002-9939-06-08527-3

The unit ball of the Hilbert space in its weak topology
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by Antonio Avilés PDF

Proc. Amer. Math. Soc. 135 (2007), 833-836 Request permission

Abstract:

We show that the unit ball of $\ell _p(\Gamma )$ in its weak topology is a continuous image of $\sigma _1(\Gamma )^\mathbb {N}$, and we deduce some combinatorial properties of its lattice of open sets which are not shared by the balls of other equivalent norms when $\Gamma$ is uncountable.

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