Timeline for Complemented subspaces in the James space
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 11, 2016 at 2:29 | comment | added | Ben W | Cool. I believe those classes all coincide for $J_p$ (the $p$th James space) when $1<p<\infty$. This is because, as Laustsen showed, $\mathcal{K}(J_p)=\mathcal{E}(J_p)$ (where $\mathcal{K}\subset\mathcal{SS},\mathcal{SCS}\subset\mathcal{E}$ denote the compact, strictly singular, strictly cosingular, and inessential operators). | |
| Jul 11, 2016 at 2:09 | vote | accept | Dongyang Chen | ||
| Jul 11, 2016 at 2:01 | answer | added | Ben W | timeline score: 2 | |
| Jul 11, 2016 at 1:50 | comment | added | Dongyang Chen | I am studying about compact operators, strictly singular operators and strictly co-singular operators on the James space. | |
| Jul 11, 2016 at 0:59 | comment | added | Ben W | No, I don't. If it is important you could try to piece it together from what fragments are available on Google books. I believe all of theorem 2.d.2 is visible there. By the way---out of curiosity, what are you studying about the James space? | |
| Jul 11, 2016 at 0:47 | comment | added | Dongyang Chen | Thanks, Ben. Question 2 may follow from the book you mentioned. But I do not have this book and so I am not sure. Do you have the electronic version of this book? | |
| Jul 11, 2016 at 0:23 | comment | added | Ben W | I have not looked carefully yet, but it seems that the answer to question 2 might also be true. Check out section 2.d in The James Forest by Helga Fetter and Berta Gamboa de Buen. Most of it is on Google books. books.google.com/books?id=GQJVVtDwx5wC&pg=PA43 | |
| Jul 10, 2016 at 23:53 | comment | added | Ben W | The answer to question 1 is yes. See the comments after Remark 2.11 in arxiv.org/abs/1401.4231 and Proposition 2.4 in acadsci.fi/mathematica/Vol36/… I do not know the answer to question 2. | |
| Jul 10, 2016 at 23:23 | history | asked | Dongyang Chen | CC BY-SA 3.0 |