Timeline for On existence of certain operators in von Neumann algebra
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 24, 2019 at 19:36 | history | edited | Dmitri Pavlov | CC BY-SA 4.0 |
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| Sep 23, 2019 at 22:41 | comment | added | Dmitri Pavlov | @Desperatemathematician: For a II_1 factor M you can construct a counterexample by taking a faithful finite trace τ on M, then ξ=τ^{1/2} is an element in the standard form of M that is a counterexample to your claim: if xξ=ξ, then (x−1)ξ=0, so rsupp(x−1)lsupp(ξ)=0, but lsupp(ξ)=lsupp(τ^{1/2})=1, hence rsupp(x−1)=0, i.e., x−1=0 and x=1. | |
| Sep 23, 2019 at 19:35 | comment | added | Robert Furber | $I$ must be countable for this to work, or else there is no nowhere vanishing $\xi$. | |
| Sep 23, 2019 at 19:09 | comment | added | sibani | @Dimitri, If I assume $M$ is the hyperfinite $\mathrm{II_{1}}$ factor, then still false!! | |
| Sep 23, 2019 at 19:08 | vote | accept | sibani | ||
| Sep 23, 2019 at 19:06 | history | answered | Dmitri Pavlov | CC BY-SA 4.0 |