Timeline for Monotone series of projections converging to 1 in von Neumann algebra
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| May 27, 2020 at 16:34 | comment | added | Tomasz Kania | That's the spectral theorem for normal elements; see Borel functional calculus in any operator algebra textbook. | |
| May 27, 2020 at 16:09 | comment | added | dreamwave | @TomaszKania - Thanks for your comment, could you explain why does {$1,u$}$''$ isomorphic to $L_\infty(\mathbb{T})$? | |
| May 27, 2020 at 15:01 | comment | added | Tomasz Kania | Take a unitary element $u$ so that $\sigma(u)=\mathbb T$, the unit circle. Then $\{1,u\}^{\prime\prime}\subset M$ is isomorphic to $L_\infty(\mathbb T)$. Can you do it in $L_\infty(\mathbb T)$? (Simply take an essentially increasing family of sets of positive measure that cover $\mathbb T$ and their indicators are the sought projections.) | |
| May 27, 2020 at 14:49 | history | edited | YCor | CC BY-SA 4.0 |
fixed English, made title more specific
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| May 27, 2020 at 14:49 | review | First posts | |||
| May 27, 2020 at 19:09 | |||||
| May 27, 2020 at 14:41 | history | asked | dreamwave | CC BY-SA 4.0 |