Timeline for Decomposition of an element as a difference of positive elements in the definition subalgebra of a weight (Takesaki)
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 16, 2022 at 20:26 | vote | accept | Andromeda | ||
| Feb 16, 2022 at 20:10 | comment | added | Andromeda | @JamieGabe I was under the impression that Takesaki was referring to lemma 1.6, chapter VII, which is basically a generalised polar decomposition. See my answer below. | |
| Feb 16, 2022 at 20:09 | comment | added | Andromeda | @MatthewDaws I am not 100% sure since I'm new to this stuff, but I posted my own proof in an answer below. | |
| Feb 16, 2022 at 20:08 | answer | added | Andromeda | timeline score: 2 | |
| Feb 16, 2022 at 19:46 | comment | added | Jamie Gabe | I believe that Takesaki meant to write in Lemma VII.1.8, that "every element in $\mathfrak m_\phi$ is the linear span of elements $y^\ast x$ with $x,y\in \mathfrak n_\phi$, the fact driven by the polarisation identity." | |
| Feb 16, 2022 at 19:22 | answer | added | Jamie Gabe | timeline score: 4 | |
| Feb 16, 2022 at 16:15 | comment | added | Matthew Daws | Interesting... Do you know how the proof works? | |
| Feb 16, 2022 at 15:06 | comment | added | Andromeda | @MatthewDaws My definition was also correct. This follows by polar decomposition (see the proof of lemma 1.8 in takesaki, chapter VII). | |
| Feb 16, 2022 at 14:14 | comment | added | Matthew Daws | I accepted an edit, which makes an important correction to the definition of $\mathfrak{m}_\varphi$ | |
| S Feb 16, 2022 at 14:14 | history | suggested | MSMalekan | CC BY-SA 4.0 |
An incorrect definition was corrected.
|
| Feb 16, 2022 at 3:41 | review | Suggested edits | |||
| S Feb 16, 2022 at 14:14 | |||||
| Feb 15, 2022 at 16:51 | history | asked | Andromeda | CC BY-SA 4.0 |