Timeline for the double dual of "little l one" sequence space
Current License: CC BY-SA 3.0
7 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Jan 3, 2016 at 14:08 | comment | added | Yemon Choi | It's worth remarking that the Carothers book, while it has some interesting parts, is a bit uneven when it comes to quality and accuracy; see the remarks in www.math.leidenuniv.nl/~mdejeu/reading_guide_carothers.pdf However, I guess that the part you refer to in your answer is Garling's use of $\beta (X_d)$ to prove the Riesz representation theorem for $C(X)^*$ ? | |
| Jan 3, 2016 at 4:16 | comment | added | Ben W | Oops about the quotient thing. I was thinking of about the duality between bounded below operators and surjective operators. So, the dual of an isomorphic embedding is a surjection. However, I forgot that we need it to be open, too, if we want a quotient map. Anyway, I have removed the quotient bit and clarified the $L_\infty$ bit. | |
| Jan 3, 2016 at 4:14 | history | edited | Ben W | CC BY-SA 3.0 |
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| Jan 3, 2016 at 4:05 | comment | added | Yemon Choi | Also, it seems off to say that every separable space is a quotient of $\ell_\infty^*$ -- that does not follow immediately from the sentence which precedes it. It is of course true that every separable Banach space is a quotient of $\ell_1$ | |
| Jan 3, 2016 at 4:04 | comment | added | Yemon Choi | When you say $\ell_\infty=L_\infty$ is the one on the left atomic and the one on the right continuous? Because if so, then the Banach spaces are isomorphic but not isometrically so | |
| Jan 3, 2016 at 2:02 | history | answered | Ben W | CC BY-SA 3.0 |