Timeline for $c_0(2^{\kappa})$ does not embed in $\ell_\infty(\kappa)$?
Current License: CC BY-SA 4.0
5 events
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| Nov 30, 2023 at 22:14 | comment | added | S Argyros | Every weakly compact subset of $l_{\infty}(\kappa)$ has topological weight at most $\kappa$. The reason is that if $W$ is weakly compact then $ (W, w)$ and $(W,w^*)$ are homeomorphic and the topological weight in the $w^*$ topology of the norm bounded subsets of $l_{\infty}(\kappa)$ is at most $\kappa$.This actually holds for every dual Banach space. Now notice that the basis of $c_0 ( \Gamma ) $ together with 0 is weakly compact with topological weight equal to the cardinality of $\Gamma$. | |
| Nov 30, 2023 at 16:40 | history | edited | M.González | CC BY-SA 4.0 |
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| Nov 30, 2023 at 16:29 | history | edited | M.González | CC BY-SA 4.0 |
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| Nov 30, 2023 at 16:23 | history | edited | M.González | CC BY-SA 4.0 |
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| Nov 30, 2023 at 16:15 | history | answered | M.González | CC BY-SA 4.0 |