Timeline for Are nuclear operators closed under extensions?
Current License: CC BY-SA 4.0
6 events
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| May 26, 2020 at 2:07 | comment | added | santker heboln | Addendum: Actually, Jochen's example shows that even if $T_i$'s are assumed to be surjective, $\theta$ may not equal $T_2$. However, if $T_i$ have dense ranges, I think $\theta$ could be "close" to $T_2$, it seems unitarily equivalent. | |
| May 24, 2020 at 22:35 | comment | added | santker heboln | I now think the conditions the $T_i$ having dense ranges for $i = 1,2,3$ and the squares commuting should give the desired equality $\theta = T_2$ in your approach. | |
| May 24, 2020 at 17:59 | comment | added | santker heboln | Indeed, I guess a more sensible assumption (to get a positive result and also in view of intended applications) would be that the squares commute. In any case, the question as stated has been answered exhaustively. Thank you (all)! | |
| May 24, 2020 at 17:43 | comment | added | Yemon Choi | @santkerheboln before you edit the question, I should point out that surjective operators on Banach spaces are nuclear if and only if they are finite-rank. So your modified question will have a positive answer for trivial reasons | |
| May 24, 2020 at 17:37 | comment | added | santker heboln | This was a quick response! In fact I just wanted to edit my question, to say that $T_1, T_2$ and $T_3$ should be surjective. Your answer is interesting nonetheless. | |
| May 24, 2020 at 17:24 | history | answered | Yemon Choi | CC BY-SA 4.0 |