THE UNIT BALL OF THE HILBERT SPACE IN ITS WEAK TOPOLOGY

@inproceedings{Avils2005THEUB,
  title={THE UNIT BALL OF THE HILBERT SPACE IN ITS WEAK TOPOLOGY},
  author={Antonio Avil{\'e}s},
  year={2005}
}
We show that the unit ball of p(Γ) in its weak topology is a continuous image of σ1(Γ), and we deduce some combinatorial properties of its lattice of open sets which are not shared by the balls of other equivalent norms when Γ is uncountable. For a set Γ and a real number 1 < p < ∞, the Banach space p(Γ) is a reflexive space, hence its unit ball is compact in the weak topology, and in fact, it is homeomorphic to the following closed subset of the Tychonoff cube [−1, 1]: B(Γ) = ⎧⎨ ⎩ ∈ [−1, 1… CONTINUE READING

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