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Banach-Alaoglu for topological vector spaces #15734

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mcdoll opened this issue Jul 28, 2022 · 0 comments
Open

Banach-Alaoglu for topological vector spaces #15734

mcdoll opened this issue Jul 28, 2022 · 0 comments
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feature-request This issue is a feature request, either for mathematics, tactics, or CI

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mcdoll commented Jul 28, 2022

We should have almost everything to prove the general Banach-Alaoglu theorem. One reference would be Chapter 8 in the book by Narici-Beckenstein. The main ingredients still missing are the completeness of the algebraic dual (Thm 8.2.9) and the equivalence of weakly bounded and weakly totally bounded (Thm 8.2.8). The proof of the Banach-Alaoglu theorem for Banach spaces might be helpful as well.
@mcdoll mcdoll added the feature-request This issue is a feature request, either for mathematics, tactics, or CI label Jul 28, 2022
@mcdoll mcdoll changed the title Banach Alaoglu for topological vector spaces Banach-Alaoglu for topological vector spaces Jul 28, 2022
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