Timeline for quasi-weakly compact operators, co-ideals of operator ideals, and Banach spaces $X$ with $X^{**}/X$ separable
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 14, 2016 at 21:42 | comment | added | Ben W | Ah, nevermind, that idea doesn't work. Conjecture 2 still wide open. | |
| May 14, 2016 at 21:34 | comment | added | Ben W | Thank you! Indeed, I have seen none of those papers (nor even heard of them). I looked at the James paper just now, and it has the following interesting theorem: If $E$ is a space with boundedly complete basis with basis constant = 1, then there exists a Banach space $X$ with shrinking basis such that $X^{**}=X+E_1$ for some isometric copy $E_1$ of $E$. I think I see a way to finish the proof of Conjecture 2 above using that fact. When I get a chance, I will take a look at the other papers. | |
| May 10, 2016 at 16:54 | comment | added | Mikhail Ostrovskii | From your question it is not clear whether you are aware of the constructions of James (Pacific J. Math., 1960), Lindenstrauss (Israel J. Math, 1971), Bellenot (J. Funct. Anal., 1982), and results of Valdivia (Israel J. Math. 1988). Some years ago I studied the construction of Bellenot, in particular I used it to construct an infinite inverse sequence of separable spaces with strictly singular quotient maps (Bull. Polish Acad. Sci. Math. 44 (1996), no. 2, 143–146). | |
| May 8, 2016 at 18:31 | history | asked | Ben W | CC BY-SA 3.0 |