Timeline for Lifting quasi-nilpotent elements in C$^*$-algebras
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 9, 2022 at 19:53 | comment | added | Douglas Somerset | Then Tatiana Shulman showed in Lifting of nilpotent contractions, Bulletin of the London Mathematical Society, Volume 40, Issue 6, December 2008, Pages 1002–1006, doi.org/10.1112/blms/bdn084 that every nilpotent contraction can be lifted to a nilpotent contraction. | |
| Apr 9, 2022 at 19:52 | comment | added | Douglas Somerset | It was shown in C. L. Olsen and G. K. Pedersen, Corona-algebras and their applications to lifting problems, Math. Scand. 64 (1989), 63-86 that every nilpotent can be lifted; and in T. A. Loring, Lifting solutions to perturbing problems in C∗-algebras, volume 8 of Fields Institute Monographs. American Mathematical Society, Providence, RI, 1997 that nilpotents can be lifted with arbitrarily small increase in norm. | |
| Apr 9, 2022 at 19:27 | comment | added | Derek | In case Akemann feels slighted, read "Akemann and Pedersen" for "Pedersen" :-) | |
| Apr 9, 2022 at 19:13 | comment | added | Derek | @DouglasSomerset I was also hoping someone who has more current experience in this area could provide supplementary information or comment on extensions. There is also work by Pedersen in lifting nilpotents using an unrelated-and non-equivalent construction, also from the 1980s or late 1970s. I have asked a colleague and student of Gerry Murphy (unfortunately no longer with us) and will comment again (or they can comment) if there is more recent information. I strongly recommend getting the BMSW monograph, as their journal publications are a bit harder to read. | |
| Apr 9, 2022 at 9:08 | vote | accept | Douglas Somerset | ||
| Apr 9, 2022 at 9:08 | comment | added | Douglas Somerset | It would be interesting to know of any developments beyond the 1982 result, but in the absence of further information the tick goes to @Derek. | |
| Apr 7, 2022 at 19:33 | comment | added | Douglas Somerset | Many thanks. I used to have a copy but I got rid of most of my books years ago, and I had forgotten this result. | |
| Apr 7, 2022 at 9:25 | history | answered | Derek | CC BY-SA 4.0 |