The Unit Ball of the Hilbert Space in Its Weak Topology
نویسنده
چکیده
We show that the unit ball of lp(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 lp(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]:
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