Timeline for A question on Grothendieck space
Current License: CC BY-SA 4.0
16 events
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| Apr 25, 2021 at 15:11 | comment | added | Onur Oktay | My purpose was actually to point out the difference between the 4 statements that are seemingly the same : 1) every weak*-null sequence in the dual is weakly null 2) every weak*-null sequence in the dual has a weakly null subsequence 3) every weak*-null sequence in the dual is weakly Cauchy 4) every weak*-null sequence in $X^{\ast}$ has weakly Cauchy subsequence The first three of those is equivalent to X being a Grothendieck space. Only the 4th is weaker, as written above. | |
| Apr 25, 2021 at 15:10 | comment | added | Onur Oktay | AlexM @TimCampion: Sorry folks, I didn't include a reference since I do not have a good reference for the whole equivalence except my notes. If I included a proof myself, the post would be longer than the question and the answer. However, as Tomasz Kania graciously pointed out, the proof is almost verbatim similar to Theorem 3.1.1 in the reference he's given. | |
| Apr 25, 2021 at 14:42 | comment | added | Tim Campion | @AlexM. I think there is a place on MO for answers in the "too long to be a comment" category which provide useful information and context for a question. I agree it would be nice to have some references. | |
| Apr 25, 2021 at 13:56 | comment | added | Onur Oktay | @Tomasz Kania: Thank you for the reference. I was not aware that there were so many open problems pertaining to Grothendieck spaces. It will be a pleasure to read through the paper, and it sure will take some time for me. | |
| Apr 25, 2021 at 13:21 | comment | added | Tomasz Kania | This is essentially Theorem 3.1.1 in arxiv.org/pdf/2102.03838.pdf | |
| Apr 25, 2021 at 10:35 | review | Low quality posts | |||
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| Apr 25, 2021 at 10:29 | comment | added | Alex M. | While your post might contain useful information (although no proof or reference is given), I don't think that it answers the question. It looks more like a (long) comment. | |
| Apr 25, 2021 at 6:53 | history | edited | Onur Oktay | CC BY-SA 4.0 |
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| Apr 25, 2021 at 5:48 | history | edited | Onur Oktay | CC BY-SA 4.0 |
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| Apr 25, 2021 at 5:28 | history | edited | Onur Oktay | CC BY-SA 4.0 |
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| S Apr 25, 2021 at 5:15 | review | Late answers | |||
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| S Apr 25, 2021 at 5:15 | review | First posts | |||
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| Apr 25, 2021 at 5:12 | history | undeleted | Onur Oktay | ||
| Apr 25, 2021 at 5:12 | history | edited | Onur Oktay | CC BY-SA 4.0 |
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| Apr 25, 2021 at 4:24 | history | deleted | Onur Oktay | via Vote | |
| Apr 25, 2021 at 4:19 | history | answered | Onur Oktay | CC BY-SA 4.0 |