Timeline for If the closed unit ball of Banach space has at least one extreme point, must the Banach space the be a dual space?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Dec 3, 2018 at 3:01 | comment | added | MSMalekan | @DirkWerner Thanks for the comment, you are right! | |
| Dec 2, 2018 at 22:03 | comment | added | Dirk Werner | @MeisamSoleimaniMalekan: I am not absolutely positive about your previous comment: Write $C[0,1]^*$ as $L_1[0,1] \oplus_1 Y$ with $Y=$ singular measures w.r.t. the Lebesgue measure. So a dual can have a non-dual $\ell_1$-direct summand. My argument: If $L_2\oplus L_1$ were a dual, it would, being separable, have the RNP, and hence $L_1$ would have the RNP, which it doesn't. | |
| Dec 2, 2018 at 16:03 | comment | added | MSMalekan | @Idonknow This is because, $X\oplus Y$ is dual iff both $X$ and $Y$ are dual. | |
| Dec 2, 2018 at 14:56 | comment | added | Idonknow | How can we prove that $L^2(\mathbb R)\oplus L^1(\mathbb R)$ is not a dual space? | |
| Dec 2, 2018 at 10:24 | history | edited | MSMalekan | CC BY-SA 4.0 |
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| Dec 2, 2018 at 9:33 | history | answered | MSMalekan | CC BY-SA 4.0 |