Timeline for comparison of two projections in a non-factor von Neumann algebra
Current License: CC BY-SA 4.0
7 events
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| Oct 29, 2020 at 16:51 | comment | added | Michael Montgomery | I suppose this can happen for small algebras like $\mathbb C \oplus \mathbb C$. What you are looking for is the comparison theorem. For a von Neumann algebra $M$ and projections $p,q$ in $M$ there exists a central projection $z$ such that $pz \preceq qz$ and $q(1-z) \preceq p(1-z)$. A nice example to think about is the von Neumann algebra of measurable essentially bounded functions from the interval $[0,1]$ to $M_2(\mathbb C)$. | |
| Oct 29, 2020 at 6:47 | comment | added | Manish Kumar | One more question: Can two non-central projections always be compared in some non-factor von Neumann algebras? | |
| Oct 29, 2020 at 6:44 | vote | accept | Manish Kumar | ||
| Oct 29, 2020 at 5:40 | history | edited | Michael Montgomery | CC BY-SA 4.0 |
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| Oct 29, 2020 at 5:02 | history | edited | Michael Montgomery | CC BY-SA 4.0 |
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| Oct 29, 2020 at 4:57 | review | First posts | |||
| Oct 29, 2020 at 6:04 | |||||
| Oct 29, 2020 at 4:56 | history | answered | Michael Montgomery | CC BY-SA 4.0 |