Timeline for Finding closed subspaces whose sum isn't closed
Current License: CC BY-SA 4.0
13 events
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| Jan 12, 2023 at 16:47 | comment | added | Gerry Myerson | Mathoverflow is not for discussions. It is for tightly targeted answers to well-posed questions. | |
| Jan 9, 2023 at 12:58 | comment | added | S Argyros | If $X$ does not have $w^*$ separable dual then for every separable subspace $Y$ of $X$ there exists a non separable $Z$ such that $Y \cap Z = 0$. Indeed choose $( g_n )$ in $X^*$ such that the subspace $Z= ( g_n )_\bot$ has trivial intersection with $Y$. The subspace $Z$ is non separable since otherwise $X^*$ is $w^*$ separable. | |
| Jan 8, 2023 at 18:26 | comment | added | Bill Johnson | In case it is not obvious to the two or three others following this thread, we should note that Theorem 3 above implies that the famous "separable quotient problem" (whether every infinite dimensional Banach space has a separable infinite dimensional quotient) is equivalent to the problem whether every separable subspace of every Banach space is quasi-complemented. | |
| Jan 8, 2023 at 10:22 | history | edited | S Argyros | CC BY-SA 4.0 |
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| Jan 6, 2023 at 17:43 | comment | added | S Argyros | I understand your point but I think that the discussion has a natural evolution. Anyone not interested on this he can simply skip it. It is so simple. | |
| Jan 6, 2023 at 17:24 | comment | added | Nik Weaver | I appreciate your interest and zeal, but going on and on with these answers is probably not appropriate for this site... | |
| Jan 6, 2023 at 17:15 | history | edited | S Argyros | CC BY-SA 4.0 |
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| Jan 6, 2023 at 15:59 | history | edited | S Argyros | CC BY-SA 4.0 |
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| Jan 6, 2023 at 15:42 | history | edited | S Argyros | CC BY-SA 4.0 |
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| Jan 6, 2023 at 15:15 | history | edited | S Argyros | CC BY-SA 4.0 |
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| Jan 6, 2023 at 15:00 | history | edited | S Argyros | CC BY-SA 4.0 |
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| Jan 6, 2023 at 14:26 | history | edited | S Argyros | CC BY-SA 4.0 |
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| Jan 6, 2023 at 14:18 | history | answered | S Argyros | CC BY-SA 4.0 |